Chiral algebra of Argyres-Douglas theory from M5 brane
Dan Xie, Wenbin Yan, Shing-Tung Yau
TL;DR
The paper identifies the 2d chiral algebras associated with Argyres-Douglas theories engineered from M5 branes, proposing a coset (for theories without flavor) and an affine Kac-Moody (for theories with a full regular puncture) realization that reproduce the 4d/2d central-charge relation and yield the Schur index as the vacuum character. It provides concrete group-theoretic realizations, establishes W-algebra minimal models for the coset case, and gives explicit affine algebras with level data for the matter case, including example computations like D2[SU(2N+1)]. The work connects these algebras to DS reduction and 3d mirrors, and outlines how to generalize to flavored irregular punctures and larger SCFTs built from AD matter. Overall, it strengthens the 4d/2d dictionary for AD theories, offering calculable tools to access operator content and Schur indices from 2d chiral algebras.
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.