$\beta$-deformed matrix models and the 2d/4d correspondence

TL;DR

This paper reviews how matrix model techniques can be applied to analyze instanton partition functions in N=2 supersymmetric gauge theories, revealing new insights through mathematical representations derived from localization results.

Contribution

It introduces a matrix model representation of instanton partition functions, enabling the use of matrix model methods to study their properties in different limits and special cases.

Findings

Matrix model integrals represent instanton partition functions effectively.

Techniques from matrix models facilitate analysis of gauge theory results.

New computational approaches for supersymmetric gauge theories are proposed.

Abstract

This is the fourth article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It describes a very useful mathematical representation of the results of the localisation computations of instanton partition functions as integrals having a form familiar from the study of matrix models. Techniques from the study of matrix models can be employed to extract important information on the instanton partition functions in various limits and special cases.