@article{behtash_kamata_martinez_schafer_skokov_2021, title={Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons}, volume={103}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/1830583}, DOI={10.1103/PhysRevD.103.056010}, abstractNote={We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.}, number={5}, journal={PHYSICAL REVIEW D}, publisher={American Physical Society (APS)}, author={Behtash, A. and Kamata, S. and Martinez, M. and Schafer, T. and Skokov, V}, year={2021}, month={Mar} }
 @article{behtash_kamata_martinez_shi_2020, title={Global flow structure and exact formal transseries of the Gubser flow in kinetic theory}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP07(2020)226}, abstractNote={A bstract In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2020}, month={Jul} }
 @article{behtash_kamata_martinez_shi_2019, title={Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow}, volume={99}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.99.116012}, abstractNote={In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory. We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energy nonhydrodynamic mode. It is demonstrated that the survival of this new mode is intrinsically related to the nonlinear mode-to-mode coupling with the shear viscous term. Finally, we comment on some possible phenomenological applications of the proposed nonhydrodynamic transport theory.}, number={11}, journal={PHYSICAL REVIEW D}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2019}, month={Jun} }
 @article{behtash_cruz-camacho_kamata_martinez_2019, title={Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma}, volume={797}, ISSN={["1873-2445"]}, DOI={10.1016/j.physletb.2019.134914}, abstractNote={For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the non-perturbative dissipative contributions quantified by the Knudsen $Kn$ and inverse Reynolds $Re^{-1}$ numbers. At any given order in the asymptotic expansion of each mode, the transport coefficients get effectively renormalized by summing over all non-perturbative sectors appearing in the trans-series. This gives an effective description of the transport coefficients that provides a new renormalization scheme with an associated renormalization group equation, going beyond the realms of linear response theory. As a result, the renormalized transport coefficients feature a transition to their equilibrium fixed point, which is a neat diagnostics of transient non-Newtonian behavior. As a proof of principle, we verify the predictions of the effective theory with the numerical solutions of their corresponding evolution equations. Our studies strongly suggest that the phenomenological success of fluid dynamics far from local thermal equilibrium is due to the transient rheological behavior of the fluid.}, journal={PHYSICS LETTERS B}, author={Behtash, Alireza and Cruz-Camacho, C. N. and Kamata, Syo and Martinez, M.}, year={2019}, month={Oct} }
 @article{cruz-camacho_behtash_martinez_2019, title={Out-of-equilibrium Gubser flow attractors}, volume={982}, ISSN={["1873-1554"]}, DOI={10.1016/j.nuclphysa.2018.10.004}, abstractNote={We discuss the non-equilibrium attractors of systems undergoing Gubser flow within kinetic theory by means of nonlinear dynamical systems. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories. These attractors are non-planar and the basin of attraction is three dimensional. We compare the asymptotic attractors of each hydrodynamic model with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. Anisotropic hydrodynamics matches, up to high numerical accuracy, the attractor of the exact theory while the other hydrodynamic theories fail to do so. Thus, anisotropic hydrodynamics is an effective theory for far-from-equilibrium fluids, which consists of the dissipative (nonperturbative) contributions at any order in the gradient expansion.}, journal={NUCLEAR PHYSICS A}, author={Cruz-Camacho, C. N. and Behtash, A. and Martinez, M.}, year={2019}, month={Feb}, pages={204–206} }
 @article{martinez_behtash_cruz-camacho_kamata_2019, title={Relating the Lyapunov exponents to transport coefficients in kinetic theory}, volume={982}, ISSN={["1873-1554"]}, DOI={10.1016/j.nuclphysa.2018.10.078}, abstractNote={In this contribution, we report our recent findings on the phenomenological applications of non-equilibrium attractors to transport phenomena in fluid dynamics. Within the kinetic theory description, we study the non-linear hydrodynamization processes of a relativistic fluid undergoing Bjorken flow. The mathematical problem of solving the Boltzmann equation with a time-dependent relaxation time is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. The constitutive relations of each non-hydrodynamic mode can be written as a multi-parameter trans-series that encodes the non-perturbative dissipative contributions quantified by the Knudsen Kn and inverse Reynolds Re−1 numbers. At a given order in the gradient expansion, we show that summing over all the non-perturbative sectors leads to a renormalized transport coefficient. The universal behavior of the renormalized shear viscosity is determined by the Lyapunov exponent and the anomalous dimension of the first moment at the stable fixed point. We comment on the relation between our findings and the physics of non-Newtonian fluids.}, journal={NUCLEAR PHYSICS A}, author={Martinez, M. and Behtash, A. and Cruz-Camacho, C. N. and Kamata, S.}, year={2019}, month={Feb}, pages={227–230} }
 @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={Abstract
          }, 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{behtash_cruz-camacho_martinez_2018, title={Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow}, volume={97}, ISSN={["2470-0029"]}, DOI={10.1103/physrevd.97.044041}, abstractNote={The non-equilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed non-planar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansion diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward effective field theory description of hydrodynamics. Our findings indicate that anisotropic hydrodynamics is an effective theory for far-from-equilibrium fluid dynamics which resums the Knudsen and inverse Reynolds numbers to all orders.}, number={4}, journal={PHYSICAL REVIEW D}, author={Behtash, Alireza and Cruz-Camacho, C. N. and Martinez, M.}, year={2018}, month={Feb} }
 @article{behtash_2018, title={More on homological supersymmetric quantum mechanics}, volume={97}, ISSN={["2470-0029"]}, DOI={10.1103/physrevd.97.065002}, abstractNote={In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for non-zero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of $\mathcal{N} = 4$ quantum mechanics with background $R$-symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The $R$-anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos (FI) parameters appear in the intersection coefficients for the relative homology of the quiver quantum mechanics resulting from dimensional reduction of $2d$ $\mathcal{N}=(2,2)$ gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in $\mathcal{N}=4$ $\mathbb{CP}^{k-1}$ model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantum mechanics is indicated.}, number={6}, journal={PHYSICAL REVIEW D}, author={Behtash, Alireza}, year={2018}, month={Mar} }
 @article{behtash_dunne_schaefer_sulejmanpasic_uensal_2017, title={Toward Picard-Lefschetz theory of path integrals, complex saddles and resurgence}, volume={2}, ISSN={["2380-2898"]}, url={http://inspirehep.net/record/1397667}, DOI={10.4310/amsa.2017.v2.n1.a3}, abstractNote={We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions.We demonstrate that complex saddle points have a natural interpretation in terms of the Picard–Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on $\mathbb{R}^3 \times S^1$, we study quantum-mechanical systems with bosonic and fermionic (Grassmann) degrees of freedom with harmonic degenerate minima, as well as (related) purely bosonic systems with harmonic nondegenerate minima. We find exact finite action non-BPS bounce and bion solutions to the holomorphic Newton equations. We find not only real solutions, but also complex solution with non-trivial monodromy, and finally complex multi-valued and singular solutions. Complex bions are necessary for obtaining the correct nonperturbative structure of these models. In the supersymmetric limit the complex solutions govern the ground state properties, and their contribution to the semiclassical expansion is necessary to obtain consistency with the supersymmetry algebra. The multi-valuedness of the action is either related to the hidden topological angle or to the resurgent cancellation of ambiguities. We also show that in the approximate multi-instanton description the integration over the complex quasi-zero mode thimble produces the most salient features of the exact solutions. While exact complex saddles are more difficult to construct in quantum field theory, the relation to the approximate thimble construction suggests that such solutions may be underlying some remarkable features of approximate bion saddles in quantum field theories.}, number={1}, journal={ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS}, author={Behtash, Alireza and Dunne, Gerald V. and Schaefer, Thomas and Sulejmanpasic, Tin and Uensal, Mithat}, year={2017}, pages={95–212} }
 @article{behtash_dunne_schaefer_sulejmanpasic_uensal_2016, title={Complexified Path Integrals, Exact Saddles, and Supersymmetry}, volume={116}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1396147}, DOI={10.1103/physrevlett.116.011601}, abstractNote={In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories.}, number={1}, journal={PHYSICAL REVIEW LETTERS}, author={Behtash, Alireza and Dunne, Gerald V. and Schaefer, Thomas and Sulejmanpasic, Tin and Uensal, Mithat}, year={2016}, month={Jan} }
 @article{behtash_sulejmanpasic_schaefer_uensal_2015, title={Hidden Topological Angles in Path Integrals}, volume={115}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1346264}, DOI={10.1103/physrevlett.115.041601}, abstractNote={We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in n f to non-integer number of flavors, reducing in the integer n f limit to a Z2 valued phase difference between dominant saddles. In N = 1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like SU(N) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semi-classical expansion. In quantum mechanics, a HTA leads to a difference in semi-classical expansion of integer and half-integer spin particles.}, number={4}, journal={PHYSICAL REVIEW LETTERS}, author={Behtash, Alireza and Sulejmanpasic, Tin and Schaefer, Thomas and Uensal, Mithat}, year={2015}, month={Jul} }
 @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} }