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

We study superconformal indices of 4d N=2 class S theories with certain irregular punctures called type I_k,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,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 (A₁,A_2n) theory. We also discuss the mixed Schur indices for the N=1 class S theories with irregular punctures.