Generalized Multiple q-Zeta Values and Characters of Vertex Algebras

TL;DR

This paper explores the connections between vertex algebra characters and generalized q-multiple zeta values, introducing new algebraic structures and conjectures in the context of mathematical physics.

Contribution

It introduces a family of multiple q-zeta values linked to Lie algebras and analyzes their role in vertex algebra characters across various physical and mathematical settings.

Findings

Character expressions in terms of generalized q-MZVs

Introduction of q-zeta values associated to Lie algebras

Conjectural properties of these q-zeta values

Abstract

We analyze certain characters of vertex algebras that can be expressed using (generalized) q-MZVs. We consider: (i) characters of vertex algebras associated to arc spaces, (ii) characters (or indices) of $\mathcal{S}$-class vertex operator algebras in 4d $\mathcal{N}=2$ SCFT, (iii) supercharacters of the $\mathcal{U}$ family of vertex algebras. Along the way we also introduce a family of multiple $q$-zeta values associated to simple Lie algebras and present their conjectural properties.