Chiral algebra of Argyres-Douglas theory from M5 brane

TL;DR

This paper explores the chiral algebras associated with Argyres-Douglas theories derived from M5 branes, revealing their structure as W algebras or affine Kac-Moody algebras depending on the singularity configuration.

Contribution

It identifies the specific chiral algebra structures for different Argyres-Douglas theories engineered from M5 branes, linking geometric singularities to algebraic structures.

Findings

Chiral algebra for theories with a single irregular singularity is a minimal W algebra.

Chiral algebra for theories with irregular and full regular singularities is an affine Kac-Moody algebra.

Schur index can be computed from the vacuum character of the associated chiral algebra.

Abstract

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d $(2,0)$ type $J$ theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of $J$ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of $J$ type. We can obtain the Schur index of these theories by computing the vacua character of the corresponding chiral algebra.