@article{cherman_jacobson_shifman_unsal_vainshtein_2023, title={Four-fermion deformations of the massless Schwinger model and confinement}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP01(2023)087}, abstractNote={A bstract We consider the massless charge- N Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a ℤ 2 subgroup of chiral symmetry for even N , hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on ℝ 2 using bosonization, and also analyze the mechanism of confinement on ℝ × S 1 , where we find that confinement is driven by fractional instantons.}, number={1}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Cherman, Aleksey and Jacobson, Theodore and Shifman, Mikhail and Unsal, Mithat and Vainshtein, Arkady}, year={2023}, month={Jan} }
@article{nguyen_tanizaki_unsal_2023, title={Study of gapped phases of 4d gauge theories using temporal gauging of the Z(N) 1-form symmetry}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP08(2023)013}, abstractNote={To study gapped phases of $4$d gauge theories, we introduce the temporal gauging of $\mathbb{Z}_N$ $1$-form symmetry in $4$d quantum field theories (QFTs), thereby defining effective $3$d QFTs with $\widetilde{\mathbb{Z}}_N\times \mathbb{Z}_N$ $1$-form symmetry. In this way, spatial fundamental Wilson and 't Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the $4$d QFT, the $\widetilde{\mathbb{Z}}_N\times \mathbb{Z}_N$ symmetry must be spontaneously broken to an order-$N$ subgroup $H$, and we can classify the $4$d gapped phases by specifying $H$. This establishes the $1$-to-$1$ correspondence between the two classification schemes for gapped phases of $4$d gauge theories: One is the conventional Wilson-'t Hooft classification, and the other is the modern classification using the spontaneous breaking of $4$d $1$-form symmetry enriched with symmetry-protected topological states.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Aug} }
@article{nguyen_tanizaki_unsal_2023, title={Winding ? and destructive interference of instantons}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP09(2023)033}, abstractNote={While the $\theta$ dependence of field theories is $2\pi$ periodic, the ground-state wavefunctions at $\theta$ and $\theta+2\pi$ often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the $\theta$ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the $2$d $\mathbb{C}P^{N-1}$ sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small $S^1$ compactification with nonzero winding $\theta$ parameter and a suitable symmetry-twisted boundary condition. This system has $N$ classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have $N$-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, which is sharp contrast to what happens when the $\theta$ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the $N$ perturbative vacua acquire different charges under the global symmetry with the activation of the winding $\theta$ angle. We also demonstrate a similar destructive interference between instanton effects in the $\mathbb{C}P^{N-1}$ quantum mechanics with the Berry phase.}, number={9}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Sep} }
@article{tanizaki_unsal_2022, title={Center vortex and confinement in Yang Mills theory and QCD with anomaly-preserving compactifications}, volume={2022}, ISSN={["2050-3911"]}, url={http://dx.doi.org/10.1093/ptep/ptac042}, DOI={10.1093/ptep/ptac042}, abstractNote={Abstract We construct an anomaly-preserving compactification of 4D gauge theories, including SU(N) Yang–Mills theory, $\mathcal {N}=1$ supersymmetric Yang–Mills theory, and quantum chromodynamics (QCD), down to 2D by turning on the ’t Hooft flux through T2. This provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and the multi-branch structure of vacua. We give a semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly-matching condition as the original 4D gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2 \times \mathbb {R}^2$ is adiabatically connected to the strong-coupling regime on $\mathbb {R}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on the ’t Hooft flux either by activating the SU(Nf)V symmetry twist for Nf = N flavors or by introducing a magnetic flux of baryon number U(1)B for arbitrary Nf flavors. In both cases, the weak-coupling center-vortex theory gives a prediction consistent with the chiral Lagrangian of 4D QCD.}, number={4}, journal={PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS}, publisher={Oxford University Press (OUP)}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Apr} }
@article{pazarba_unsal_2022, title={Cluster Expansion and Resurgence in the Polyakov Model}, volume={128}, ISSN={["1079-7114"]}, DOI={10.1103/PhysRevLett.128.151601}, abstractNote={In the Polyakov model, a nonperturbative mass gap is formed at leading-order semiclassics by instanton effects. By using the notions of critical points at infinity, cluster expansion, and Lefschetz thimbles, we show that a third-order effect in semiclassics gives an imaginary ambiguous contribution to the mass gap, which is supposed to be real and unambiguous. This is troublesome for the original analysis, and it is difficult to resolve this issue directly in quantum field theory (QFT). However, we find a new compactification of the Polyakov model to quantum mechanics, by using a background 't Hooft flux. The compactification has the merit of remembering the monopole instantons of the full QFT within Born-Oppenheimer approximation, while the periodic compactification does not. In the quantum mechanical limit, we prove the resurgent cancellation of the ambiguity in three-instanton sector against ambiguity in the Borel resummation of the perturbation theory around one instanton. Assuming that this result holds in QFT, we provide a large-order asymptotics of perturbation theory around perturbative vacuum and instanton.}, number={15}, journal={PHYSICAL REVIEW LETTERS}, author={Pazarba, Cihan and Unsal, Mithat}, year={2022}, month={Apr} }
@article{unsal_2022, title={Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP03(2022)119}, abstractNote={The dimension of the Hilbert space of QFT scales exponentially with the volume of the space in which the theory lives, yet in supersymmetric theories, one can define a graded dimension (such as the supersymmetric index) that counts just the number of bosonic minus fermionic ground states. Can we make this observation useful in non-supersymmetric QFTs in four dimensions? In this work, we construct symmetry graded state sums for a variety of non-supersymmetric theories. Among the theories we consider is one that is remarkably close to QCD: Yang--Mills theory with $N_f = N_c$ fundamental Dirac fermions and one adjoint Weyl fermion, QCD(F/adj). This theory can be obtained from SQCD by decoupling scalars and carry exactly the same anomalies. Despite the existence of fundamental fermions, the theory possess an exact 0-form color-flavor center (CFC) symmetry for a particular grading/twist under which Polyakov loop is a genuine order parameters. By a two-loop analysis, we prove that CFC-symmetry remains unbroken at small $\beta $ due to grading. Chiral symmetry is spontaneously broken within the domain of validity of semi-classics on $\mathbb R^3 \times S^1$ in a pattern identical to $N_f=N_c$ SQCD on $\mathbb R^4$ and the two regimes are adiabatically connected. The vacuum structures of the theory on $\mathbb R^4$ and $\mathbb R^3 \times S^1$ are controlled by the same mixed 't Hooft anomaly condition, implying a remarkable persistent order.}, number={3}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Unsal, Mithat}, year={2022}, month={Mar} }
@article{pazarbasi_unsal_2022, title={Polyakov model in 't Hooft flux background: a quantum mechanical reduction with memory}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP08(2022)116}, abstractNote={We construct a compactification of Polyakov model on $T^2 \times \mathbb R $ down to quantum mechanics which remembers non-perturbative aspects of field theory even at an arbitrarily small area. Standard compactification on small $T^2 \times \mathbb R $ possesses a unique perturbative vacuum (zero magnetic flux state), separated parametrically from higher flux states, and the instanton effects do not survive in the Born-Oppenheimer approximation. By turning on a background magnetic GNO flux in co-weight lattice corresponding to a non-zero 't Hooft flux, we show that $N$-degenerate vacua appear at small torus, and there are $N-1$ types of flux changing instantons between them. We construct QM instantons starting with QFT instantons using the method of replicas. For example, $SU(2)$ gauge theory with flux reduces to the double-well potential where each well is a fractional flux state. Despite the absence of a mixed anomaly, the vacuum structure of QFT and the one of QM are continuously connected. We also compare the quantum mechanical reduction of the Polyakov model with the deformed Yang-Mills, by coupling both theories to TQFTs. In particular, we compare the mass spectrum for dual photons and energy spectrum in the QM limit. We give a detailed description of critical points at infinity in the semi-classical expansion, and their role in resurgence structure.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Pazarbasi, Cihan and Unsal, Mithat}, year={2022}, month={Aug} }
@article{tanizaki_unsal_2022, title={Semiclassics with 't Hooft flux background for QCD with 2-index quarks}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/2086495}, DOI={10.1007/JHEP08(2022)038}, abstractNote={A bstract We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ 2 × T 2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T 2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large- N orientifold equivalence between QCD(Sym/ASym) and $$ \mathcal{N} $$ N = 1 supersymmetric SU( N ) Yang-Mills theory.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Aug} }
@article{sueishi_kamata_misumi_unsal_2021, title={Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S-1}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP07(2021)096}, abstractNote={A bstract We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S 1 . We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N -minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even N and global inconsistency for odd N . By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Sueishi, Naohisa and Kamata, Syo and Misumi, Tatsuhiro and Unsal, Mithat}, year={2021}, month={Jul} }
@article{nguyen_tanizaki_unsal_2021, title={Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory}, volume={104}, ISSN={["2470-0029"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85114421307&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.104.065003}, abstractNote={Pure Yang-Mills theory in 2 spacetime dimensions shows exact Casimir scaling. Thus there are infinitely many string tensions, and this has been understood as a result of non-propagating gluons in 2 dimensions. From ordinary symmetry considerations, however, this richness in the spectrum of string tensions seems mysterious. Conventional wisdom has it that it is the center symmetry that classifies string tensions, but being finite it cannot explain infinitely many confining strings. In this note, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a non-invertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in 3 and 4 dimensions.}, number={6}, journal={PHYSICAL REVIEW D}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Sep} }
@article{nguyen_tanizaki_unsal_2021, title={Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality}, volume={03}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1839639}, DOI={10.1007/JHEP03(2021)238}, abstractNote={A bstract We study a 3d lattice gauge theory with gauge group U(1) N− 1 ⋊ S N , which is obtained by gauging the S N global symmetry of a pure U(1) N− 1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU( N ) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤ N , we observe that the string tensions do not obey the N -ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1) N− 1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W -bosons, such non-invertible symmetries are explicitly broken so that the N -ality rule should emerge in the deep infrared regime.}, number={3}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Mar} }
@article{unsal_2021, title={Strongly coupled QFT dynamics via TQFT coupling}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP11(2021)134}, abstractNote={We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb Z_N$ topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb Z_N$ TQFT structure arises naturally from turning on a classical background field for a $\mathbb Z_N$ 0- or 1-form global symmetry. In $SU(N)$ Yang-Mills theory coupled to $\mathbb Z_N$ TQFT, the non-perturbative expansion parameter is $\exp[-S_I/N]= \exp[-{8 \pi^2}/{g^2N}]$ both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original $SU(N)$ theory, we must use $PSU(N)$ bundle and lift configurations (critical points at infinity) for which there is no obstruction back to $SU(N)$. These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on $T^3 \times S^1_L$ can be interpreted as tunneling events in the 't Hooft flux background in the $PSU(N)$ bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-$N$ and instanton analysis. We derive the mass gap at $\theta=0$ and gaplessness at $\theta=\pi$ in $\mathbb{CP}^{1}$ model, and mass gap for arbitrary $\theta$ in $\mathbb{CP}^{N-1}, N \geq 3$ on $\mathbb R^2$.}, number={11}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Unsal, Mithat}, year={2021}, month={Nov} }
@article{sueishi_kamata_misumi_unsal_2020, title={On exact-WKB analysis, resurgent structure, and quantization conditions}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP12(2020)114}, abstractNote={There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: Saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schr\"{o}dinger equation. In this work, based on the quantization conditions obtained from the exact-WKB method, we determine the relations between the two formalism and in particular show how the two Stokes phenomena are connected to each other: the Stokes phenomenon leading to the ambiguous contribution of different sectors of the path integral formulation corresponds to the change of the "topology" of the Stoke curves in the exact-WKB analysis. We also clarify the equivalence of different quantization conditions including Bohr-Sommerfeld, path integral and Gutzwiller's ones. In particular, by reorganizing the exact quantization condition, we improve Gutzwiller analysis in a crucial way by bion contributions (incorporating complex periodic paths) and turn it into an exact result. Furthermore, we argue the novel meaning of quasi-moduli integral and provide a relation between the Maslov index and the intersection number of Lefschetz thimbles.}, number={12}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Sueishi, Naohisa and Kamata, Syo and Misumi, Tatsuhiro and Unsal, Mithat}, year={2020}, month={Dec} }
@article{kanazawa_unsal_2020, title={Quantum distillation in QCD}, volume={102}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.102.034013}, abstractNote={We propose a grading protocol that assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the image of quantum distillation in terms of (nondynamical) flavor holonomy dependence of (dynamical) gauge-holonomy potentials, in QCD with ${N}_{f}={N}_{c}$ fundamental and one massive adjoint fermion on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$. The compactified theory possesses an exact zero-form color-flavor center symmetry for a special choice of flavor holonomy (under which Polyakov loop is charged), despite the absence of one-form center symmetry. We prove that the color-flavor center symmetry is stable at small $\ensuremath{\beta}$. This is the opposite of the high-temperature limit of thermal theory and a dramatic manifestation of quantum distillation. We show chiral symmetry breaking at small ${S}^{1}$ and that the vacuum structure of the theory on ${\mathbb{R}}^{4}$ and ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ are controlled by the same mixed 't Hooft anomaly condition.}, number={3}, journal={PHYSICAL REVIEW D}, author={Kanazawa, Takuya and Unsal, Mithat}, year={2020}, month={Aug} }
@article{cherman_shifman_unsal_2019, title={Bose-Fermi cancellations without supersymmetry}, volume={99}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.99.105001}, abstractNote={We show that adjoint QCD features very strong Bose-Fermi cancellations in the large $N$ limit, despite the fact that it is manifestly non-supersymmetric. The difference between the bosonic and fermionic densities of states in large $N$ adjoint QCD turns out to have a `two-dimensional' scaling $\sim \exp{(\sqrt{\ell E})}$ for large energies $E$ in finite spatial volume, where $\ell$ is a length scale associated with the curvature of the spatial manifold. In particular, all Hagedorn growth cancels, and so does the growth $\exp{(V^{1/4} E^{3/4})}$ expected in a standard local 4d theory in spatial volume $V$. In these ways, large $N$ adjoint QCD, a manifestly non-supersymmetric theory, acts similarly to supersymmetric theories. We also show that at large $N$, the vacuum energy of multi-flavor adjoint QCD is non-negative and exponentially small compared to the UV cutoff with several natural regulators.}, number={10}, journal={PHYSICAL REVIEW D}, author={Cherman, Aleksey and Shifman, Mikhail and Unsal, Mithat}, year={2019}, month={May} }
@article{aitken_cherman_unsal_2019, title={Dihedral symmetry in SU (N) Yang-Mills theory}, volume={100}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.100.085004}, abstractNote={We point out that charge conjugation and coordinate reflection symmetries do not commute with the center symmetry of $SU(N)$ Yang-Mills (YM) theory when $N>2$. As a result, for generic values of the $\ensuremath{\theta}$ angle, the group of discrete 0-form symmetries of YM theory on, e.g., the spacetime manifold ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ includes the dihedral group ${D}_{2N}$, which is non-Abelian for $N>2$. At $\ensuremath{\theta}=\ensuremath{\pi}$, the non-Abelian factor in the symmetry group is enhanced to ${D}_{4N}$ due to discrete 't Hooft anomaly considerations. We illustrate these results in YM theory as well as in a simple quantum mechanical model, where we study representation theory as a function of the $\ensuremath{\theta}$ angle.}, number={8}, journal={PHYSICAL REVIEW D}, author={Aitken, Kyle and Cherman, Aleksey and Unsal, Mithat}, year={2019}, month={Oct} }
@article{misumi_tanizaki_unsal_2019, title={Fractional theta angle, 't Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model}, volume={2019}, ISSN={["1029-8479"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85068760265&partnerID=MN8TOARS}, DOI={10.1007/JHEP07(2019)018}, abstractNote={A bstract This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge- q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on ℝ 2 and its compactification to ℝ× S L 1 . We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e i θ / Nq , which provides the Nq -branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large- N limit of the Schwinger model with twisted boundary conditions satisfy volume independence.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Misumi, Tatsuhiro and Tanizaki, Yuya and Unsal, Mithat}, year={2019}, month={Jul} }
@article{bergner_piemonte_unsal_2018, title={Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP11(2018)092}, abstractNote={This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions in the adjoint representation. These theories have the remarkable property that confinement and discrete chiral symmetry breaking can persist at weak coupling on small (non-thermal) $\mathbb R^3 \times S^1$. This work presents a lattice investigation of Yang-Mills with one adjoint Majorana fermion, $\mathcal N=1$ super Yang-Mills, and opens the prospect to understand a number of non-perturbative phenomena, such as the mechanism of confinement, mass gap, chiral and center symmetry realizations both in lattice and continuum analytically. We study the compactification of this theory on the lattice with periodic and thermal boundary conditions. We provide numerical evidence for the conjectured absence of the phase transitions with periodic boundary conditions for sufficiently light lattice fermions (stability of center-symmetry), suppression of the chiral transition, and also provide a diagnostic for abelian vs. non-abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions. In numerical and perturbative investigations we identify the role of the lattice artefacts that become relevant in the very small radius regime, and resolve some puzzles in the naive comparison between continuum and lattice.}, number={11}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Bergner, Georg and Piemonte, Stefano and Unsal, Mithat}, year={2018}, month={Nov} }
@article{sulejmanpasic_unsal_2018, title={Aspects of perturbation theory in quantum mechanics: The BenderWu MATHEMATICA (R) package}, volume={228}, ISSN={["1879-2944"]}, DOI={10.1016/j.cpc.2017.11.018}, abstractNote={We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender–Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use Mathematica ® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10–30 s, and 250 orders in 1–2 h) and enables practical study of a large class of problems in Quantum Mechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters. Program Title: BenderWu Program Files doi: http://dx.doi.org/10.17632/vpg2zsbryc.1 Licensing provisions: CC By 4.0 Programming language: Wolfram Mathematica Nature of problem: In 1D quantum mechanics, a perturbative expansions are known to generically be divergent. An analysis of such problems was so far limited to a case-by-case basis. The Mathematica package presented here allows a quick computation and analysis of all such 1D quantum mechanical problems. Solution method: The program uses a general recursive relation, inspired by the works of Bender and Wu [1], which allows quick computation of the perturbative data. References Carl M. Bender, Tai Tsun Wu, Phys. Rev. 184 (1969) 1231–1260 * Items marked with an asterisk are only required for new versions of programs previously published in the CPC Program Library.}, journal={COMPUTER PHYSICS COMMUNICATIONS}, author={Sulejmanpasic, Tin and Unsal, Mithat}, year={2018}, month={Jul}, pages={273–289} }
@article{kozcaz_sulejmanpasic_tanizaki_unsal_2018, title={Cheshire Cat Resurgence, Self-Resurgence and Quasi-Exact Solvable Systems}, volume={364}, ISSN={["1432-0916"]}, url={http://inspirehep.net/record/1487463}, DOI={10.1007/s00220-018-3281-y}, abstractNote={We explore a one parameter $${\zeta}$$ -deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of $${\zeta}$$ , the lowest $${\zeta}$$ states turn out to be exactly solvable for DSG—a feature known as Quasi-Exact-Solvability (QES)—and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like dependence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles. We show that the convergence is dictated by the quantization of the hidden topological angle. Further, we argue that the QES systems can be linked to the exact cancellation of real and complex non-perturbative saddles to all orders in the semi-classical expansion. We also show that the entire resurgence structure remains encoded in the analytic properties of the $${\zeta}$$ -deformation, even though exactly at integer values of $${\zeta}$$ the mechanism of resurgence is obscured by the lack of ambiguity in both the Borel sum of the perturbation theory as well as the non-perturbative contributions. In this way, all of the characteristics of resurgence remains even when its role seems to vanish, much like the lingering grin of the Cheshire Cat. We also show that the perturbative series is Self-resurgent—a feature by which there is a one-to-one relation between the early terms of the perturbative expansion and the late terms of the same expansion—which is intimately connected with the Dunne–Ünsal relation. We explicitly verify that this is indeed the case.}, number={3}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Kozcaz, Can and Sulejmanpasic, Tin and Tanizaki, Yuya and Unsal, Mithat}, year={2018}, month={Dec}, pages={835–878} }
@article{behtash_dunne_schafer_sulejmanpasic_unsal_2018, title={Critical points at infinity, non-Gaussian saddles, and bions}, volume={06}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1665487}, DOI={10.1007/jhep06(2018)068}, abstractNote={It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of of Picard-Lefschetz theory. In this work we compute the contribution from non-BPS multi-instanton configurations, such as instanton-anti-instanton $[{I}\bar{I}]$ pairs, and argue that these contributions should be interpreted as exact critical points at infinity. The Lefschetz thimbles associated with such critical points have a specific structure arising from the presence of non-Gaussian, quasi-zero mode (QZM), directions. When fermion degrees of freedom are present, as in supersymmetric theories, the effective bosonic potential can be written as the sum of a classical and a quantum potential. We show that in this case the semi-classical contribution of the critical point at infinity vanishes, but there is a non-trivial contribution that arises from its associated non-Gaussian QZM-thimble. This approach resolves several puzzles in the literature concerning the semi-classical contribution of correlated $[{I}\bar{I}]$ pairs. It has the surprising consequence that the configurations that dominate the expansion of observables, and the critical points that define the Lefschetz thimble decomposition need not be the same, a feature not present in the traditional Picard-Lefschetz approach.}, number={6}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Behtash, Alireza and Dunne, Gerald V and Schafer, Thomas and Sulejmanpasic, Tin and Unsal, Mithat}, year={2018}, month={Jun} }
@article{dunne_tanizaki_unsal_2018, title={Quantum distillation of Hilbert spaces, semi-classics and anomaly matching}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1658917}, DOI={10.1007/JHEP08(2018)068}, abstractNote={A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect "quantum distillation". Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under $S^1$ compactification. We revisit this point via the 't Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $\mathbb{R}^d$ and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model $\mathrm{Gr}(N,M)$. We also discuss the connection of quantum distillation with large-$N$ volume independence and flavor-momentum transmutation.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Dunne, Gerald V. and Tanizaki, Yuya and Unsal, Mithat}, year={2018}, month={Aug} }
@article{aitken_cherman_unsal_2018, title={Vacuum structure of Yang-Mills theory as a function of theta}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP09(2018)030}, abstractNote={A bstract It is believed that in SU( N ) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ . We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on ℝ 3 × S 1 . We find that while observables are indeed N-branched functions of θ, there are only ≈ N/ 2 locally-stable candidate vacua for any given θ . We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ , and gather evidence for the conjecture that these spinodal points are present even in the ℝ 4 limit.}, number={9}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Aitken, Kyle and Cherman, Aleksey and Unsal, Mithat}, year={2018}, month={Sep} }
@article{komargodski_sulejmanpasic_unsal_2018, title={Walls, anomalies, and deconfinement in quantum antiferromagnets}, volume={97}, DOI={10.1103/physrevb.97.054418}, abstractNote={We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum anti-ferromagnets. In the presence of $\mathbb{Z}_2$ preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the Valence Bond Solid (VBS) phase of quantum magnets. We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is $SU(2)_1$ WZW). Either way the fundamental scalar particles (i.e. spinons) which are confined in the bulk are deconfined on the domain-wall. This $\mathbb{Z}_2$ phase can be realized either with spin-1/2 on a rectangular lattice, or spin-1 on a square lattice. In both cases the domain wall contains spin-1/2 particles (which are absent in the bulk). We discuss the possible relation to recent lattice simulations of domain walls in VBS. We further generalize the discussion to Abrikosov-Nielsen-Olsen (ANO) vortices in a dual superconductor of the Abelian-Higgs model in 3+1 dimensions, and to the easy-plane limit of anti-ferromagnets. In the latter case the wall can undergo a variant of the BKT transition (consistent with the anomalies) while the bulk is still gapped. The same is true for the easy-axis limit of anti-ferromagnets. We also touch upon some analogies to Yang-Mills theory.}, number={5}, journal={Physical Review B}, author={Komargodski, Z. and Sulejmanpasic, T. and Unsal, M.}, year={2018} }
@article{sulejmanpasic_shao_sandvik_unsal_2017, title={Confinement in the Bulk, Deconfinement on the Wall: Infrared Equivalence between Compactified QCD and Quantum Magnets}, volume={119}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.119.091601}, abstractNote={In a spontaneously dimerized quantum antiferromagnet, spin-$1/2$ excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-Abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.}, number={9}, journal={PHYSICAL REVIEW LETTERS}, author={Sulejmanpasic, Tin and Shao, Hui and Sandvik, Anders W. and Unsal, Mithat}, year={2017}, month={Sep} }
@article{cherman_sen_unsal_wagman_yaffe_2017, title={Order Parameters and Color-Flavor Center Symmetry in QCD}, volume={119}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.119.222001}, abstractNote={Common lore suggests that $N$-color QCD with massive quarks has no useful order parameters that can be nontrivial at zero baryon density. However, such order parameters do exist when there are ${n}_{f}$ quark flavors with a common mass and $d\ensuremath{\equiv}gcd({n}_{f},N)>1$. These theories have a ${\mathbb{Z}}_{d}$ color-flavor center symmetry arising from intertwined color center transformations and cyclic flavor permutations. The symmetry realization depends on the temperature, baryon chemical potential, and value of ${n}_{f}/N$, with implications for conformal window studies and dense quark matter.}, number={22}, journal={PHYSICAL REVIEW LETTERS}, author={Cherman, Aleksey and Sen, Srimoyee and Unsal, Mithat and Wagman, Michael L. and Yaffe, Laurence G.}, year={2017}, month={Nov} }
@article{kanazawa_unsal_yamamoto_2017, title={Phases of circle-compactified QCD with adjoint fermions at finite density}, volume={96}, ISSN={["2470-0029"]}, DOI={10.1103/physrevd.96.034022}, abstractNote={We study chemical-potential dependence of confinement and mass gap in QCD with adjoint fermions in spacetime with one spatial compact direction. By calculating the one-loop effective potential for the Wilson line in the presence of chemical potential, we show that a center-symmetric phase and a center-broken phase alternate when the chemical potential in unit of the compactification scale is increased. In the center-symmetric phase we use semiclassical methods to show that photons in the magnetic bion plasma acquire a mass gap that grows with the chemical potential as a result of anisotropic interactions between monopole-instantons. For the neutral fermionic sector which remains gapless perturbatively, there are two possibilities at non-perturbative level. Either to remain gapless (unbroken global symmetry), or to undergo a novel superfluid transition through a four-fermion interaction (broken global symmetry). If the latter is the case, this leads to an energy gap of quarks proportional to a new nonperturbative scale $L^{-1}\exp[-1/(g^4 \mu L)]$, where $L$ denotes the circumference of $S^1$, the low-energy is described as a Nambu-Goldstone mode associated with the baryon number, and there exists a new type of BEC-BCS crossover of the diquark pairing as a function of the compactification scale at small chemical potential.}, number={3}, journal={PHYSICAL REVIEW D}, author={Kanazawa, Takuya and Unsal, Mithat and Yamamoto, Naoki}, year={2017}, month={Aug} }
@article{basar_dunne_unsal_2017, title={Quantum geometry of resurgent perturbative/nonperturbative relations}, ISSN={["1029-8479"]}, DOI={10.1007/jhep05(2017)087}, abstractNote={For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain $$ \mathcal{N} $$ = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.}, number={5}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Basar, Gokce and Dunne, Gerald V. and Unsal, Mithat}, year={2017}, month={May} }
@inbook{dunne_ünsal_2017, place={Pisa, Italy}, series={CRM Series}, title={WKB and resurgence in the Mathieu equation}, ISBN={9788876426124 9788876426131}, url={http://dx.doi.org/10.1007/978-88-7642-613-1_6}, DOI={10.1007/978-88-7642-613-1_6}, abstractNote={In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expansion in the weak coupling regime produces resurgent trans-series expressions which exhibit precise relations between different instanton sectors. Indeed, the perturbative expansion encodes all orders of the multi-instanton expansion, an explicit realization of the general concept of “resurgence”. We also discuss the transition from weak to strong coupling, an explicit realization of “instanton condensation”.}, booktitle={Resurgence, Physics and Numbers}, publisher={Scuola Normale Superiore}, author={Dunne, Gerald V. and Ünsal, Mithat}, editor={Fauvet, F. and Manchon, D. and Marmi, S. and Sauzin, D.Editors}, year={2017}, pages={249–298}, collection={CRM Series} }
@article{cherman_schafer_unsal_2016, title={Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD}, volume={117}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1449992}, DOI={10.1103/physrevlett.117.081601}, abstractNote={We show that there exists a special compactification of QCD on $\mathbb{R}^3 \times S^1$ in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation $m_{\pi}^2 f_{\pi}^2 = m_q \langle \bar{q} q \rangle$. Abelian duality, monopole operators, and flavor-twisted boundary conditions, or a background flavor holonomy, play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole-instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons". We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large $S^1$, and yield strong support for adiabatic continuity between the small-$S^1$ and large-$S^1$ regimes. We also find concrete microscopic connections between ${\cal N}=1$ and ${\cal N}=2$ supersymmetric gauge theory dynamics and non-supersymmetric QCD dynamics.}, number={8}, journal={PHYSICAL REVIEW LETTERS}, author={Cherman, Aleksey and Schafer, Thomas and Unsal, Mithat}, year={2016}, month={Aug} }
@article{dunne_unsal_2016, title={Deconstructing zero: resurgence, supersymmetry and complex saddles}, ISSN={["1029-8479"]}, DOI={10.1007/jhep12(2016)002}, abstractNote={We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence. We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle π), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles. In either case, despite the fact that the ground state energy is zero to all orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E (N, g). We illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.}, number={12}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Dunne, Gerald V. and Unsal, Mithat}, year={2016}, month={Dec} }
@article{dunne_unsal_2016, title={New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence}, volume={66}, ISSN={["1545-4134"]}, DOI={10.1146/annurev-nucl-102115-044755}, abstractNote={We present a broad conceptual introduction to some new ideas in nonperturbative quantum field theory (QFT) that have led to progress toward an understanding of quark confinement in gauge theories and, more broadly, toward a nonperturbative continuum definition of QFTs. We first present exact orbifold equivalences of supersymmetric and nonsupersymmetric QFTs in the large-N limit and exact equivalences of large-N theories in infinite volume to large-N theories in finite volume, or even at a single point. We discuss principles by which calculable QFTs are continuously connected to strong-coupling QFTs, allowing understanding of the physics of confinement or the absence thereof. We discuss the role of particular saddle solutions, termed bions, in weak-coupling calculable regimes. The properties of bions motivate an extension of semiclassical methods used to evaluate functional integrals to include families of complex saddles (Picard–Lefschetz theory). This analysis leads us to the resurgence program, which may provide a framework for combining divergent perturbation series with semiclassical instanton and bion/renormalon contributions. This program could provide a nonperturbative definition of the path integral.}, journal={ANNUAL REVIEW OF NUCLEAR AND PARTICLE SCIENCE, VOL 66}, author={Dunne, Gerald V. and Unsal, Mithat}, year={2016}, pages={245–272} }
@article{cherman_dorigoni_ünsal_2015, title={Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles}, volume={2015}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP10(2015)056}, DOI={10.1007/JHEP10(2015)056}, abstractNote={Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about non-perturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected. Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations. To demonstrate some of these ideas, we study the SU(N) principal chiral model (PCM), a two dimensional asymptotically free matrix field theory which has no instantons, because the relevant homotopy group is trivial. Adiabatic continuity is used to reach a weakly coupled regime where NP effects are calculable. We then use resurgence theory to uncover the existence and role of novel ‘fracton’ saddle points, which turn out to be the fractionalized constituents of previously observed unstable ‘uniton’ saddle points. The fractons play a crucial role in the physics of the PCM, and are responsible for the dynamically generated mass gap of the theory. Moreover, we show that the fracton-anti-fracton events are the weak coupling realization of ’t Hooft’s renormalons, and argue that the renormalon ambiguities are systematically cancelled in the semi-classical expansion. Our results motivate the conjecture that the semi-classical expansion of the path integral can be geometrized as a sum over Lefschetz thimbles.}, number={10}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Cherman, Aleksey and Dorigoni, Daniele and Ünsal, Mithat}, year={2015}, month={Oct}, pages={56} }
@article{dunne_ünsal_2015, title={Resurgence and dynamics of O(N) and Grassmannian sigma models}, volume={2015}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP09(2015)199}, DOI={10.1007/JHEP09(2015)199}, abstractNote={We study the non-perturbative dynamics of the two dimensional O(N ) and Grassmannian sigma models by using compactification with twisted boundary conditions on $$ \mathbb{R}\times {S}^1 $$ , semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on $$ {\mathbb{R}}^2 $$ , which we call 2d-saddles. On $$ \mathbb{R}\times {S}^1 $$ , the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o(N ) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O(N ) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO(N ) gauge theory on $$ {\mathbb{R}}^3\times {S}^1 $$ . The Grassmannian sigma models Gr(N, M ) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr(N, M ), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.}, number={9}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Dunne, Gerald V. and Ünsal, Mithat}, year={2015}, month={Sep}, pages={199} }
@article{cherman_koroteev_ünsal_2015, title={Resurgence and holomorphy: From weak to strong coupling}, volume={56}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.4921155}, DOI={10.1063/1.4921155}, abstractNote={We analyze the resurgence properties of finite-dimensional exponential integrals which are prototypes for partition functions in quantum field theories. In these simple examples, we demonstrate that perturbation theory, even at arbitrarily weak coupling, fails as the argument of the coupling constant is varied. It is well-known that perturbation theory also fails at stronger coupling. We show that these two failures are actually intimately related. The formalism of resurgent transseries, which takes into account global analytic continuation properties, fixes both problems and provides an arbitrarily accurate description of exact result for any value of coupling. This means that strong coupling results can be deduced by using merely weak coupling data. Finally, we give another perspective on resurgence theory by showing that the monodromy properties of the weak coupling results are in precise agreement with the monodromy properties of the strong-coupling expansions, obtained using analysis of the holomorphy structure of Picard-Fuchs equations.}, number={5}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Cherman, Aleksey and Koroteev, Peter and Ünsal, Mithat}, year={2015}, month={May}, pages={053505} }
@article{behtash_poppitz_sulejmanpasic_ünsal_2015, title={The curious incident of multi-instantons and the necessity of Lefschetz thimbles}, volume={2015}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP11(2015)175}, DOI={10.1007/JHEP11(2015)175}, abstractNote={We show that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the “separation” quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study $$ \mathcal{N}=2 $$ extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton-anti-instanton amplitude (naively calculated) seems to contribute to the ground state energy. We show, however, that the instanton-anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively of the same sign and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles due to their relative Hidden Topological Angles (HTAs). This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescription for higher order semi-classics, but a necessary one. This deduction seems to be universal and applicable to both supersymmetric and non-supersymmetric theories. In conclusion we speculate that similar conspiracies are responsible for the non-formation of certain molecular contributions in theories where instantons have more than two fermionic zeromodes and do not contribute to the superpotential.}, number={11}, journal={Journal of High Energy Physics}, publisher={Springer Nature}, author={Behtash, Alireza and Poppitz, Erich and Sulejmanpasic, Tin and Ünsal, Mithat}, year={2015}, month={Nov}, pages={175} }
@article{anber_ünsal_2014, title={QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry}, volume={2014}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP12(2014)107}, DOI={10.1007/JHEP12(2014)107}, abstractNote={We study the thermal confinement/deconfinement and non-thermal quantum phase transitions or rapid cross-overs in QCD and QCD-like theories in external magnetic fields. At large magnetic fields, while the contribution of gauge fluctuations to Wilson-line potential remains unaltered at one-loop order, the contribution of fermions effectively becomes two lower dimensional and is enhanced by the density of states of the lowest Landau level (LLL). In a spatial compactification and for heavy adjoint fermions, this enhancement leads to a calculable zero temperature quantum phase transition on R^3*S^1 driven by a competition between the center-destabilizing gauge contribution and center-stabilizing LLL fermions. We also show that at a (formal) asymptotically large magnetic field, the adjoint fermions with arbitrarily large but fixed mass stabilize the center symmetry. This is an exotic case of simultaneous non-decoupling of large mass fermions (due to the enhancement by the LLL density of states) and decoupling from the low energy effective field theory. This observation has important implications for both Hosotani mechanism, for which gauge symmetry "breaking" occurs, and large-N volume independence (Eguchi-Kawai reduction), for which gauge structure is never "broken". Despite sounding almost self-contradictory, we carefully explain the physical scales entering the problem, double-meaning of unbroken center symmetry and how a clash is avoided. We also identify, for both thermal and spatial compactification, the jump in magnetic susceptibility as an order parameter for the deconfinement transition. The predictions of our analysis are testable by using current lattice techniques.}, number={12}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Anber, Mohamed M. and Ünsal, Mithat}, year={2014}, month={Dec}, pages={107} }
@article{dunne_uensal_2014, title={Uniform WKB, multi-instantons, and resurgent trans-series}, volume={89}, ISSN={["1550-2368"]}, DOI={10.1103/physrevd.89.105009}, abstractNote={We illustrate the physical significance and mathematical origin of resurgent trans-series expansions for energy eigenvalues in quantum mechanical problems with degenerate harmonic minima, by using the uniform WKB approach. We provide evidence that the perturbative expansion, combined with a global eigenvalue condition, contains all information needed to generate all orders of the nonperturbative multi-instanton expansion. This provides a dramatic realization of the concept of resurgence, whose structure is naturally encoded in the resurgence triangle. We explain the relation between the uniform WKB approach, multi-instantons, and resurgence theory. The essential idea applies to any perturbative expansion, and so is also relevant for quantum field theories with degenerate minima which can be continuously connected to quantum mechanical systems.}, number={10}, journal={PHYSICAL REVIEW D}, author={Dunne, Gerald V. and Uensal, Mithat}, year={2014}, month={May} }
@article{basar_dunne_ünsal_2013, title={Resurgence theory, ghost-instantons, and analytic continuation of path integrals}, volume={2013}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP10(2013)041}, DOI={10.1007/JHEP10(2013)041}, abstractNote={A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost-anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.}, number={10}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Basar, Gökçe and Dunne, Gerald V. and Ünsal, Mithat}, year={2013}, month={Oct} }
@article{poppitz_schäfer_ünsal_2013, title={Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups}, volume={2013}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP03(2013)087}, DOI={10.1007/JHEP03(2013)087}, abstractNote={Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N_c) gauge theory for arbitrary N_c, and theories without a center symmetry, such as G_2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-instantons generate attraction among the eigenvalues of the Wilson line. This is counter-acted by neutral bions --- topological excitations which generate eigenvalue repulsion for all simple groups. The transition is driven by the competition between these three effects. We study the transition in more detail for the gauge groups SU(N_c), N_c>2, and G_2. In the case of G_2, there is no change of symmetry, but the expectation value of the Wilson line exhibits a discontinuity. We also examine the effect of the theta-angle on the phase transition and critical temperature T_c(theta). The critical temperature is a multi-branched function, which has a minimum at theta=pi as a result of topological intereference.}, number={3}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Schäfer, Thomas and Ünsal, Mithat}, year={2013}, month={Mar} }
@article{anber_poppitz_ünsal_2012, title={2d affine XY-spin model/4d gauge theory duality and deconfinement}, volume={2012}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP04(2012)040}, DOI={10.1007/JHEP04(2012)040}, abstractNote={We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2)and SU(2)/Z_2 gauge theories, compactified on a small spatial circle R^(1,2) x S^1, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R^2 x T^2. Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N) gauge theories with n_f >=1 adjoint Weyl fermions.}, number={4}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Anber, Mohamed M. and Poppitz, Erich and Ünsal, Mithat}, year={2012}, month={Apr} }
@article{poppitz_schäfer_ünsal_2012, title={Continuity, deconfinement, and (super) Yang-Mills theory}, volume={2012}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP10(2012)115}, DOI={10.1007/JHEP10(2012)115}, abstractNote={We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m → ∞ and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m → 0. In the m-L plane, there is a line of center-symmetry changing phase transitions. In the limit m → ∞, this transition takes place at L c = 1/T c , where T c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m = 0, the critical compactification scale L c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center-symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m = 0, and via the Bogomolnyi-Zinn-Justin (BZJ) prescription in non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N = 1 theories — the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ . We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.}, number={10}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Schäfer, Thomas and Ünsal, Mithat}, year={2012}, month={Oct}, pages={115} }
@article{dunne_ünsal_2012, title={Resurgence and trans-series in Quantum Field Theory: the CPN−1 model}, volume={2012}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP11(2012)170}, DOI={10.1007/JHEP11(2012)170}, abstractNote={This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from mathematics are resurgence theory, the trans-series framework, and Borel-Écalle resummation. The ideas from QFT use continuity on ${{\mathbb{R}}^1}\times \mathbb{S}_L^1$ , i.e., the absence of any phase transition as N → ∞ or rapid-crossovers for finite-N, and the small-L weak coupling limit to render the semi-classical sector well-defined and calculable. We classify semi-classical configurations with actions 1/N (kink-instantons), 2/N (bions and bi-kinks), in units where the 2d instanton action is normalized to one. Perturbation theory possesses the IR-renormalon ambiguity that arises due to non-Borel summability of the large-orders perturbation series (of Gevrey-1 type), for which a microscopic cancellation mechanism was unknown. This divergence must be present because the corresponding expansion is on a singular Stokes ray in the complexified coupling constant plane, and the sum exhibits the Stokes phenomenon crossing the ray. We show that there is also a non-perturbative ambiguity inherent to certain neutral topological molecules (neutral bions and bion-anti-bions) in the semiclassical expansion. We find a set of “confluence equations” that encode the exact cancellation of the two different type of ambiguities. There exists a resurgent behavior in the semi-classical trans-series analysis of the QFT, whereby subleading orders of exponential terms mix in a systematic way, canceling all ambiguities. We show that a new notion of “graded resurgence triangle” is necessary to capture the path integral approach to resurgence, and that graded resurgence underlies a potentially rigorous definition of general QFTs. The mass gap and the Θ angle dependence of vacuum energy are calculated from first principles, and are in accord with large-N and lattice results.}, number={11}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Dunne, Gerald V. and Ünsal, Mithat}, year={2012}, month={Nov}, pages={170} }
@article{argyres_ünsal_2012, title={The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects}, volume={2012}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP08(2012)063}, DOI={10.1007/JHEP08(2012)063}, abstractNote={We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.}, number={8}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Argyres, Philip C. and Ünsal, Mithat}, year={2012}, month={Aug} }
@article{poppitz_ünsal_2011, title={Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected}, volume={2011}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP07(2011)082}, DOI={10.1007/JHEP07(2011)082}, abstractNote={We study four-dimensional $ \mathcal{N} = 2 $ supersymmetricpure-gauge (Seiberg-Witten) theory and its $ \mathcal{N} = 1 $ mass perturbation by using compactification on $ {\mathbb{S}^1} \times {\mathbb{R}^3} $ . It is well known that on $ {\mathbb{R}^4} $ (or at large $ {\mathbb{S}^1} $ size L) the perturbed theory realizes confinement through monopole or dyon condensation. At small $ {\mathbb{S}^1} $ , we demonstrate that confinement is induced by a generalization of Polyakov’s three-dimensional instanton mechanism to a locally four-dimensionaltheory — the magneticbion mechanism — which also applies to a large class of nonsupersymmetric theories. Using a large-vs. small-L Poisson duality, we show that the two mechanisms of confinement, previously thought to be distinct, are in fact continuously connected.}, number={7}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Ünsal, Mithat}, year={2011}, month={Jul} }
@article{poppitz_ünsal_2010, title={Comments on large-N volume independence}, volume={2010}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP01(2010)098}, DOI={10.1007/JHEP01(2010)098}, abstractNote={We study aspects of the large-N volume independence on R**3 x L**G, where L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L**G agrees with the one on the continuum S**1. For Wilson parameter set to one and G>=2, the two analyses agree. One-loop radiative corrections to Wilson-line masses are finite, reminiscent of the UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories. Even for theories with G=1, volume independence in QCD(adj) may be guaranteed to work by tuning one low-energy effective field theory parameter. Within the parameter space of the theory, at most three operators of the 3d effective field theory exhibit one-loop UV-sensitivity. This opens the analytical prospect to study 4d non-perturbative physics by using lower dimensional field theories (d=3, in our example).}, number={1}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Ünsal, Mithat}, year={2010}, month={Jan} }
@article{ünsal_yaffe_2010, title={Large-N volume independence in conformal and confining gauge theories}, volume={2010}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP08(2010)030}, DOI={10.1007/JHEP08(2010)030}, abstractNote={Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on $ {\mathbb{R}^{d - k}} \times {\left( {{S^1}} \right)^k} $ are independent of the S 1 radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on $ {\mathbb{R}^d} $ , flowstoan IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $ {\mathbb{R}^{d - k}} \times {\left( {{S^1}} \right)^k} $ . In other words, finite volume effects are 1/N suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In $ \mathcal{N} = 4 $ supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on $ {\mathbb{R}^{4 - k}} \times {\left( {{S^1}} \right)^k} $ has a moduli space which contains points with all possible realizations of center symmetry. Large N QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.}, number={8}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Ünsal, Mithat and Yaffe, Laurence G.}, year={2010}, month={Aug} }
@article{catterall_galvez_ünsal_2010, title={Realization of center symmetry in two adjoint flavor large-N Yang-Mills}, volume={2010}, ISSN={1029-8479}, url={http://dx.doi.org/10.1007/JHEP08(2010)010}, DOI={10.1007/JHEP08(2010)010}, abstractNote={We report on the results of numerical simulations of $SU(N)$ lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with $\Gamma$ sites in each direction in the large-$N$ limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of $\Gamma$, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume $2^4$. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit $N\to\infty$, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.}, number={8}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Catterall, Simon and Galvez, Richard and Ünsal, Mithat}, year={2010}, month={Aug} }
@article{shifman_ünsal_2009, title={Confinement in Yang–Mills: Elements of a Big Picture}, volume={186}, ISSN={0920-5632}, url={http://dx.doi.org/10.1016/j.nuclphysbps.2008.12.053}, DOI={10.1016/j.nuclphysbps.2008.12.053}, abstractNote={This is a combined and slightly expanded version of talks delivered at 14th International QCD Conference “QCD 08,” 7-12th July 2008, Montpellier, France, the International Conference “Quark Confinement and the Hadron Spectrum,” Mainz, Germany, September 1-6, 2008 (Confinement 08), and the International Conference “Approaches to Quantum Chromodynamics,” Oberwölz, Austria, September 7-13, 2008.}, journal={Nuclear Physics B - Proceedings Supplements}, publisher={Elsevier BV}, author={Shifman, M. and Ünsal, Mithat}, year={2009}, month={Jan}, pages={235–242} }
@article{catterall_kaplan_ünsal_2009, title={Exact lattice supersymmetry}, volume={484}, ISSN={0370-1573}, url={http://dx.doi.org/10.1016/j.physrep.2009.09.001}, DOI={10.1016/j.physrep.2009.09.001}, abstractNote={We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at non-zero lattice spacing. These include the especially interesting case of N=4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and on orbifold–deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine-tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.}, number={3-4}, journal={Physics Reports}, publisher={Elsevier BV}, author={Catterall, Simon and Kaplan, David B. and Ünsal, Mithat}, year={2009}, month={Nov}, pages={71–130} }
@article{poppitz_ünsal_2009, title={Index theorem for topological excitations on R3× S1and Chern-Simons theory}, volume={2009}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2009/03/027}, DOI={10.1088/1126-6708/2009/03/027}, abstractNote={We derive an index theorem for the Dirac operator in the background of various topological excitations on an R3 × S1 geometry. The index theorem provides more refined data than the APS index for an instanton on R4 and reproduces it in decompactification limit. In the R3 limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associated with the boundary Dirac operator. Neither topological charge nor η-invariant is typically an integer, however, the non-integer parts cancel to give an integer-valued index. Our derivation is based on axial current non-conservation — an exact operator identity valid on any four-manifold — and on the existence of a center symmetric, or approximately center symmetric, boundary holonomy (Wilson line). We expect the index theorem to usefully apply to many physical systems of interest, such as low temperature (large S1, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S1 of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S1). In QCD-like and chiral gauge theories, the index theorem should shed light into the nature of topological excitations responsible for chiral symmetry breaking and the generation of mass gap in the gauge sector. We also show that imposing chirally-twisted boundary condition in gauge theories with fermions induces a Chern-Simons term in the infrared. This suggests that some QCD-like gauge theories should possess components with a topological Chern-Simons phase in the small S1 regime.}, number={03}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Poppitz, Erich and Ünsal, Mithat}, year={2009}, month={Mar}, pages={027–027} }
@article{shifman_ünsal_2009, title={Multiflavor QCD∗ on R3×S1: Studying transition from Abelian to non-Abelian confinement}, volume={681}, ISSN={0370-2693}, url={http://dx.doi.org/10.1016/j.physletb.2009.10.060}, DOI={10.1016/j.physletb.2009.10.060}, abstractNote={The center-stabilized multiflavor QCD* theories formulated on R_3 x S_1 exhibit both Abelian and non-Abelian confinement as a function of the S_1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S_1), we show occurence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (\chi SB). Unlike one-flavor theories where there is no phase transition in r(S_1), the multiflavor theories possess a single phase transition associated with breaking of the continuous chiral symmetry. We conjecture that the scale of the \chi SB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.}, number={5}, journal={Physics Letters B}, publisher={Elsevier BV}, author={Shifman, M. and Ünsal, M.}, year={2009}, month={Nov}, pages={491–494} }
@article{kovtun_ünsal_yaffe_2007, title={Volume independence in large Nc QCD-like gauge theories}, volume={2007}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2007/06/019}, DOI={10.1088/1126-6708/2007/06/019}, abstractNote={Volume independence in large $\Nc$ gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large $\Nc$ orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large $\Nc$ ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large $\Nc$ equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large $\Nc$ QCD in infinite volume.}, number={06}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Kovtun, Pavel and Ünsal, Mithat and Yaffe, Laurence G}, year={2007}, month={Jun}, pages={019–019} }
@article{ünsal_2006, title={Supersymmetric deformations of type IIB matrix model as matrix regularization of Script N = 4 SYM}, volume={2006}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2006/04/002}, DOI={10.1088/1126-6708/2006/04/002}, abstractNote={We construct a $\mathcal{Q}=1$ supersymmetry and $U(1)^5$ global symmetry preserving deformation of the type IIB matrix model. This model, without orbifold projection, serves as a nonperturbative regularization for $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four Euclidean dimensions. Upon deformation, the eigenvalues of the bosonic matrices are forced to reside on the surface of a hypertorus. We explicitly show the relation between the noncommutative moduli space of the deformed matrix theory and the Brillouin zone of the emergent lattice theory. This observation makes the transmutation of the moduli space into the base space of target field theory clearer. The lattice theory is slightly nonlocal, however the nonlocality is suppressed by the lattice spacing. In the classical continuum limit, we recover the $\mathcal{N}=4$ SYM theory. We also discuss the result in terms of D-branes and interpret it as collective excitations of D(-1) branes forming D3 branes.}, number={04}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Ünsal, Mithat}, year={2006}, month={Apr}, pages={002–002} }
@article{ünsal_2006, title={Twisted supersymmetric gauge theories and orbifold lattices}, volume={2006}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2006/10/089}, DOI={10.1088/1126-6708/2006/10/089}, abstractNote={We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the $\mathcal{N}=4$ SYM in $d=4$, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group, and the exact supersymmetry of the lattice is indeed the nilpotent scalar supersymmetry of the twisted versions. We also introduce twisting in terms of spin groups of finite point subgroups of $R$-symmetry and spacetime symmetry.}, number={10}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Ünsal, Mithat}, year={2006}, month={Oct}, pages={089–089} }
@article{kaplan_ünsal_2005, title={A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges}, volume={2005}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2005/09/042}, DOI={10.1088/1126-6708/2005/09/042}, abstractNote={We formulate supersymmetric Euclidean spacetime Ad* lattices whose classical continuum limits are U(N) supersymmetric Yang-Mills theories with sixteen supercharges in d=1,2,3 and 4 dimensions. This family includes the especially interesting N=4 supersymmetry in four dimensions, as well as a Euclidean path integral formulation of Matrix Theory on a one dimensional lattice.}, number={09}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Kaplan, David B and Ünsal, Mithat}, year={2005}, month={Sep}, pages={042–042} }
@article{ünsal_2005, title={Compact gauge fields for supersymmetric lattices}, volume={2005}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2005/11/013}, DOI={10.1088/1126-6708/2005/11/013}, abstractNote={We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as compact formulations by using the polar decomposition of the complex link fields. In particular, the gauge part of the supersymmetric lattice action is the standard Wilson action. This formulation facilitates the construction of gauge invariant operators.}, number={11}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Ünsal, Mithat}, year={2005}, month={Nov}, pages={013–013} }
@article{kovtun_ünsal_yaffe_2005, title={Necessary and sufficient conditions for non-perturbative equivalences of large Nc orbifold gauge theories}, volume={2005}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2005/07/008}, DOI={10.1088/1126-6708/2005/07/008}, abstractNote={Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.}, number={07}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Kovtun, Pavel and Ünsal, Mithat and Yaffe, Laurence G}, year={2005}, month={Jul}, pages={008–008} }
@article{ünsal_2005, title={Regularization of non-commutative SYM by orbifolds with discrete torsion and SL(2,z) duality}, volume={2005}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2005/12/033}, DOI={10.1088/1126-6708/2005/12/033}, abstractNote={We construct a nonperturbative regularization for Euclidean noncommutative supersymmetric Yang-Mills theories with four ( = (2,2)) , eight ( = (4,4)) and sixteen ( = (8,8)) supercharges in two dimensions. The construction relies on orbifolds with discrete torsion, which allows noncommuting space dimensions to be generated dynamically from zero dimensional matrix model in the deconstruction limit. We also nonperturbatively prove that the twisted topological sectors of ordinary supersymmetric Yang-Mills theory are equivalent to a noncommutative field theory on the topologically trivial sector with reduced rank and quantized noncommutativity parameter. The key point of the proof is to reinterpret 't Hooft's twisted boundary condition as an orbifold with discrete torsion by lifting the lattice theory to a zero dimensional matrix theory.}, number={12}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Ünsal, Mithat}, year={2005}, month={Dec}, pages={033–033} }
@article{erlich_hong_unsal_2004, title={Matrix Models, Monopoles and Modified Moduli}, volume={2004}, ISSN={1029-8479}, url={http://dx.doi.org/10.1088/1126-6708/2004/09/024}, DOI={10.1088/1126-6708/2004/09/024}, abstractNote={Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of = 1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an = 2 nonrenormalization theorem which is inherited by these = 1 theories. Specializing to the case Nf = Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.}, number={09}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Erlich, Joshua and Hong, Sungho and Unsal, Mithat}, year={2004}, month={Sep}, pages={024–024} }