# Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement

## TL;DR

This paper explores the relationships between certain 4D $ ext{N}=2$ SCFTs, their indices, and 2D TQFT, revealing universal patterns and RG flows to highly supersymmetric theories.

## Contribution

It introduces a TQFT framework to relate Schur indices of AD theories to class $ ext{S}$ theories and uncovers universal RG flows to maximally supersymmetric SCFTs.

## Key findings

- Schur indices of AD theories relate to class $ ext{S}$ theories via simple transformations.
- TQFT expressions reveal $S$-duality actions on flavor symmetries.
- AD theories can flow to SCFTs with thirty-two supercharges.

## Abstract

We study certain exactly marginal gaugings involving arbitrary numbers of Argyres-Douglas (AD) theories and show that the resulting Schur indices are related to those of certain Lagrangian theories of class $\mathcal{S}$ via simple transformations. By writing these quantities in the language of 2D topological quantum field theory (TQFT), we easily read off the $S$-duality action on the flavor symmetries of the AD quivers and also find expressions for the Schur indices of various classes of exotic AD theories appearing in different decoupling limits. The TQFT expressions for these latter theories are related by simple transformations to the corresponding quantities for certain well-known isolated theories with regular punctures (e.g., the Minahan-Nemeschansky $E_6$ theory and various generalizations). We then reinterpret the TQFT expressions for the indices of our AD theories in terms of the topology of the corresponding 3D mirror quivers, and we show that our isolated AD theories generically admit renormalization group (RG) flows to interacting superconformal field theories (SCFTs) with thirty-two (Poincar\'e plus special) supercharges. Motivated by these examples, we argue that, in a sense we make precise, the existence of RG flows to interacting SCFTs with thirty-two supercharges is generic in a far larger class of 4D $\mathcal{N}=2$ SCFTs arising from compactifications of the 6D $(2,0)$ theory on surfaces with irregular singularities.