On the chiral algebra of Argyres-Douglas theories and S-duality

TL;DR

This paper analyzes the chiral algebra of the Argyres-Douglas $(A_3,A_3)$ theory, revealing its generators, OPEs, and symmetries, and connecting these to S-duality and the theory's conformal structure.

Contribution

It identifies the minimal chiral algebra generators for the $(A_3,A_3)$ theory and demonstrates their unique OPEs, linking algebraic structure to S-duality and conformal data.

Findings

Identified minimal chiral algebra generators for $(A_3,A_3)$

Established consistent OPEs with index and Higgs ring

Found automorphism group reflecting S-duality symmetry

Abstract

We study the two-dimensional chiral algebra associated with the simplest Argyres-Douglas type theory with an exactly marginal coupling, i.e., the $(A_3,A_3)$ theory. Near a cusp in the space of the exactly marginal deformations (i.e., the conformal manifold), the theory is well-described by the $SU(2)$ gauge theory coupled to isolated Argyres-Douglas theories and a fundamental hypermultiplet. In this sense, the $(A_3,A_3)$ theory is an Argyres-Douglas version of the $\mathcal{N}=2$ $SU(2)$ conformal QCD. By studying its Higgs branch and Schur index, we identify the minimal possible set of chiral algebra generators for the $(A_3,A_3)$ theory, and show that there is a unique set of closed OPEs among these generators. The resulting OPEs are consistent with the Schur index, Higgs branch chiral ring relations, and the BRST cohomology conjecture. We then show that the automorphism group of the chiral algebra we constructed contains a discrete group $G$ with an $S_3$ subgroup and a homomorphism $G\to S_4 \times {\bf Z}_2$. This result is consistent with the S-duality of the $(A_3,A_3)$ theory.