2023 article
Orbifolds of lattice vertex algebras
Bakalov, B., Elsinger, J., Kac, V. G., & Todorov, I. (2023, June 14). JAPANESE JOURNAL OF MATHEMATICS.
author keywords: regular vertex algebra; lattice vertex algebra; theta function; modular transformation; orbifold algebra; twisted module
open access via arxiv.org (repository)
Source: Web Of Science
Added: July 3, 2023
To a positive-definite even lattice Q, one can associate the lattice vertex algebra VQ, and any automorphism σ of Q lifts to an automorphism of VQ. In this paper, we investigate the orbifold vertex algebra V , which consists of the elements of VQ fixed under σ, in the case when σ has prime order. We describe explicitly the irreducible V -modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible V -modules. We consider in detail the cases when the order of σ is 2 or 3, as well as the case of permutation orbifolds.