2d TQFT structure of the superconformal indices with outer-automorphism twists

TL;DR

This paper explores the superconformal indices of 4d theories derived from 6d N=(2,0) theories with outer-automorphism twists, revealing a connection to deformed 2d Yang-Mills and twisted Macdonald polynomials.

Contribution

It establishes a novel link between superconformal indices with outer-automorphism twists and deformed 2d Yang-Mills theory involving twisted affine root systems.

Findings

Indices correspond to partition functions of deformed 2d Yang-Mills

The gauge group is S-dual to the fixed subgroup of b3 under c2

Deformed indices involve Macdonald polynomials of twisted affine root systems

Abstract

We study the superconformal indices of 4d theories coming from 6d N=(2,0) theory of type \Gamma on a Riemann surface, with the action of the outer-automorphism \sigma in the trace. We find that the indices are given by the partition function of a deformed 2d Yang-Mills on the Riemann surface with gauge group G which is S-dual to the subgroup of \Gamma fixed by \sigma. In the 2-parameter deformed version, we find that it is governed not by Macdonald polynomials of type G, but by Macdonald polynomials associated to twisted affine root systems.