Chiral algebra of the Argyres-Douglas theory from M5 branes

Dan Xie,Wenbin Yan,Shing-Tung Yau

doi:10.1103/physrevd.103.065003

Abstract

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 branes. 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.

Highlights

In the past few years, it has been found that certain observables of four-dimensional N 1⁄4 2 superconformal field theories (SCFTs) can be identified with observables of two-dimensional conformal field theories
Those 4D/2D correspondences include the match between the 4D sphere partition function and the correlator of 2D Liouville theory [1], the match between the trace of 4D quantum monodromy and the character of certain module of 2D chiral algebra [2,3,4,5]
2D chiral algebras constructed from 4D SCFTs are identified with known 2D models; see [5,6,7,8,9,10,11,12,13]

Summary

INTRODUCTION

In the past few years, it has been found that certain observables of four-dimensional N 1⁄4 2 superconformal field theories (SCFTs) can be identified with observables of two-dimensional conformal field theories. Those 4D/2D correspondences include the match between the 4D sphere partition function and the correlator of 2D Liouville theory [1], the match between the trace of 4D quantum monodromy and the character of certain module of 2D chiral algebra [2,3,4,5]. We consider two types of AD theories engineered from M5 brane and propose that their chiral algebras take the following form:. The chiral algebra is conjectured to be the affine Kac-Moody algebra,

AD THEORY WITHOUT FLAVOR SYMMETRY

ARGYRES-DOUGLAS MATTER