On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra

Abstract

We compute the Schur index of Argyres-Douglas theories of type $(A_{N-1},A_{M-1})$ with surface operators inserted, via the Higgsing prescription proposed by D. Gaiotto, L. Rastelli and S. S. Razamat. These surface operators are obtained by turning on position-dependent vacuum expectation values of operators in a UV theory which can flow to the Argyres-Douglas theories. We focus on two series of $(A_{N-1},A_{M-1})$ theories; one with $\gcd (N,M)=1$ and the other with $M=N(k-1)$ for an integer $k\ge 2$. For these two series of Argyres-Douglas theories, our results are identical to the characters of non-vacuum modules of the associated 2d chiral algebras, which explicitly confirms a remarkable correspondence recently discovered by C. Cordova, D. Gaiotto and S.-H. Shao.

18+13 pages, typo corrected in v3

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Cited by in corpus (13)

• Superconformal surfaces in four dimensions
• 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
• Surface defects, flavored modular differential equations and modularity
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• A new rank-2 Argyres-Douglas theory
• Closed form fermionic expressions for the Macdonald index
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• An infrared bootstrap of the Schur index with surface defects
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs