The superconformal index of theories of class $\cal S$

TL;DR

This paper reviews the superconformal index in N=2 supersymmetric gauge theories of class S, highlighting its computational advantages and its relation to a new topological field theory associated with Riemann surfaces.

Contribution

It introduces a novel topological field theory representation of the superconformal index for class S theories, facilitating duality checks.

Findings

Superconformal index is simpler to compute than instanton partition functions.

Index admits a new topological field theory representation.

Allows nontrivial tests of dualities in N=2 theories.

Abstract

This is the 8th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. The article reviews the superconformal index. It is often simpler to calculate than instanton partition functions, but nevertheless allows one to perform many nontrivial checks of conjectured dualities. It turns out to admit a representation in terms of a new type of topological field theory associated to the Riemann surfaces $C$ parameterising the class $\cal S$ theories.