Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT

Abstract

We study superconformal indices of 4d N = 2 class S theories with certain irregular punctures called type I-k,I-N. This class of theories include generalized Argyres-Douglas theories of type (A(k-1), A(N-1)) and more. We conjecture the superconformal indices in certain simplified limits based on the TQFT structure of the class S theories by writing an expression for the wave function corresponding to the puncture I-k,I-N. We write the Schur limit of the wave function when k and N are coprime. When k = 2, we also conjecture a closed-form expression for the Hall-Littlewood index and the Macdonald index for odd N. From the index, we argue that certain short-multiplet which can appear in the OPE of the stress-energy tensor is absent in the (A(1), A(2n),) theory. We also discuss the mixed Schur indices for the N = 1 class S theories with irregular punctures.