A review on instanton counting and W-algebras

TL;DR

This review explains how to compute instanton partition functions in N=2 supersymmetric gauge theories, highlighting their relation to equivariant cohomology, instanton moduli spaces, and conformal field theory symmetries.

Contribution

It provides a comprehensive overview of instanton counting methods and their connection to W-algebras and conformal field theory symmetries.

Findings

Instanton partition functions can be expressed as sums over equivariant cohomology bases.

The relationship between instanton moduli space symmetries and conformal field theory is reviewed.

The review consolidates known results linking gauge theory instantons to algebraic structures.

Abstract

This is the third article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. It is explained how to compute the instanton partition functions. The results can be written as sums over bases for the equivariant cohomology of instanton moduli spaces. The known results relating the symmetries of these spaces to the symmetries of conformal field theory are reviewed.