On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT

TL;DR

This paper explores S-duality of the 4d ${ m extbf{N}=2}$ superconformal index on Lens spaces by reformulating it as a 2d topological quantum field theory correlation function, revealing new duality insights.

Contribution

It demonstrates S-duality for the superconformal index on Lens spaces by expressing it as a 2d TFT correlation function, without fully identifying the TFT.

Findings

S-duality holds on a specific slice of the fugacity space.

Reformulation of the index resembles a 2d TFT correlation function.

Provides a new perspective on superconformal indices and dualities.

Abstract

We consider the 4d superconformal index for ${\cal N}=2$ gauge theories on $S^1 \times L(r,1)$, where $L(r,1)$ is a Lens space. We focus on a one-parameter slice of the three-dimensional fugacity space and in that sector we show S-duality. We do so by rewriting the index in a way that resembles a correlation function of a 2d TFT, which however, we do not identify.