Quasi-lisse vertex algebras and modular linear differential equations

2016/10/19 by Tomoyuki Arakawa, Arakawa, Tomoyuki, Kazuya Kawasetsu +1 · 9 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1610.05865

Abstract

We introduce a notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance property, in the sense that it satisfies a modular linear differential equation. As an application we obtain the explicit character formulas of simple affine vertex algebras associated with the Deligne exceptional series at level -h^\vee/6-1, which express the homogeneous Schur indices of 4d SCFTs studied by Beem, Lemos, Liendo, Peelaers, Rastelli and van Rees, as quasi-modular forms.

Cited by

• Generalised 4d Partition Functions and Modular Differential Equations
• Generalized Schur limit, modular differential equations and quantum monodromy traces
• Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules
• Associated Varieties of Ordinary Modules over Quasi-Lisse Vertex Algebras
• Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch
• Graded Unitarity in the SCFT/VOA Correspondence
• Index from a point
• Cyclotomic level maps and associated varieties of simple affine vertex algebras
• Generalized Schur partition functions and RG flows

Related

• Vertex algebras related to regular representations of SL₂
• Spectral flow, twisted modules and MLDE of quasi-lisse vertex algebras
• A new quasi-lisse affine vertex algebra of type D₄
• Associated Varieties of Ordinary Modules over Quasi-Lisse Vertex Algebras
• Modular linear differential equations of fourth order and minimal W-algebras