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

TL;DR

This paper computes superconformal indices of 4d N=2 class S theories with irregular punctures, including generalized Argyres-Douglas theories, using TQFT structures and conjectured formulas, revealing insights into operator spectra.

Contribution

It introduces conjectured superconformal index formulas for a broad class of theories with irregular punctures, expanding understanding of their TQFT structure and operator content.

Findings

Derived wave functions for irregular punctures in superconformal indices.

Conjectured explicit formulas for Schur, Hall-Littlewood, and Macdonald indices.

Identified absence of certain short multiplets in specific theories.

Abstract

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 $(A_1, A_{2n})$ theory. We also discuss the mixed Schur indices for the N=1 class S theories with irregular punctures.