On the correspondence between surface operators in Argyres-Douglas theories and modules of chiral algebra

A bstract 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 ≥ 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.