Quasi-lisse vertex algebras and modular linear differential equations

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.

18 pages, v4

Cited by in corpus (9)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Surface Defects and Chiral Algebras
• VOAs labelled by complex reflection groups and 4d SCFTs
• Braided tensor categories of admissible modules for affine Lie algebras
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Schur correlation functions on $S^3\times S^1$
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Singular support of a vertex algebra and the arc space of its associated scheme