# On Irregular Singularity Wave Functions and Superconformal Indices

## TL;DR

This paper extends the computation of superconformal indices for Argyres-Douglas theories using irregular singularity wave functions, providing explicit formulas and exploring their symmetries and RG flow encodings.

## Contribution

It generalizes irregular singularity wave functions to SU(N) and derives closed-form Schur indices for a broad class of AD SCFTs, enhancing understanding of their structure and symmetries.

## Key findings

- Closed-form Schur indices for (A_{N-1}, A_{N(n-1)-1}) AD theories
- Identification of discrete symmetries in superconformal indices
- Encoding of RG flows within the superconformal index framework

## Abstract

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the Schur indices of all (A_{N-1}, A_{N(n-1)-1}) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the (A_N, A_M) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.