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

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 $G\to S_4\times {\mathbf{Z}}_2$. This result is consistent with the S-duality of the $(A_3,A_3)$ theory.

25 pages, 2 figures

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• Schur correlation functions on $S^3\times S^1$
• A slow review of the AGT correspondence
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Deformation quantizations from vertex operator algebras
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• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• Lectures on chiral algebras of $\mathcal{N}⩾2$ superconformal field theories
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Vanishing short multiplets in rank one 4d/5d SCFTs