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

We study superconformal indices of 4d $$ mathcal{n}=2 $$ 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. fromtheindex,wearguethatcertainshort-multipletwhichcanappearintheopeof the stress-energy tensor is absent in the (a 1 , a 2n ) theory. we also discuss the mixed schur indices for the $$ mathcal{n}=1 $$ class $$ mathcal{s} $$ theories with irregular punctures.