The superconformal index of N=1 class S fixed points

TL;DR

This paper studies the superconformal index of four-dimensional N=1 theories from M5 branes on curves, revealing a TQFT structure and connections to SU(2) Yang-Mills theory, extending known N=2 results.

Contribution

It introduces a TQFT framework for the N=1 superconformal index, generalizing the N=2 case and relating fixed points to mathematical structures in Yang-Mills theory.

Findings

Index has a TQFT structure similar to N=2 theories

Proves infrared equivalence of fixed points via index

Links fixed points to SU(2) Yang-Mills mathematics

Abstract

We investigate the superconformal index of four-dimensional N=1 superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving N=2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the N=2 index. The TQFT structure leads to an expression for the index of all class S fixed points in terms of the index of the N=2 theories. Calculations of spectral data using the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve.