Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

TL;DR

This paper proves a conjecture linking supersymmetric Wilson loops in N=4 SYM to a Gaussian matrix model, and extends the analysis to N=2 theories on a four-sphere, providing new formulas for their expectation values.

Contribution

It establishes a localization framework for gauge theories on a four-sphere, deriving explicit matrix model formulas for supersymmetric Wilson loops in N=4 and N=2 theories.

Findings

Confirmed the conjecture relating Wilson loops to Gaussian matrix models.

Derived new matrix model formulas for N=2 and N=2* theories.

Computed partition functions for these theories on a four-sphere.

Abstract

We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2 and the N=2* supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2 superconformal gauge theory is treated similarly.