Abstract
We compute the Schur index of Argyres-Douglas theories of type (AN −1,AM −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 (AN −1, AM −1) theories; one with gcd(N, M) = 1 and the other with M = N (k − 1) for an integer k ≥ 2. Our results are identified with 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.
Highlights
The relevant 2d theory is a topological quantum field theory (TQFT) called the q-deformed Yang-Mills theory on C
These surface operators are obtained by turning on positiondependent vacuum expectation values of operators in a UV theory which can flow to the Argyres-Douglas theories
This correspondence states that, for any 4d N = 2 SCFT, the space of local operators contributing to the Schur index is equipped with the structure of a chiral algebra, or equivalently, a vertex operator algebra (VOA)
Summary
We here give a brief review of the Schur index of 4d N = 2 SCFTs with and without surface operator insertions.
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