Matrix models for 5d super Yang-Mills

TL;DR

This paper studies matrix models from 5d super Yang-Mills theory on S^5, analyzing their behavior at weak and strong coupling limits, and compares results with higher-dimensional theories and holographic predictions.

Contribution

It provides a saddle-point analysis of the matrix model in large-N limit, revealing scaling behaviors and matching supersymmetric Wilson loop results with AdS/CFT calculations.

Findings

At weak coupling, free-energy scales as N^2.

At strong coupling with one hypermultiplet, free-energy scales as N^3.

Wilson loop results match AdS/CFT predictions under certain conditions.

Abstract

In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. In general it is not possible to find an analytic solution, but at the weak and the strong limits of the 't Hooft coupling there are dramatic simplifications that allows us to extract most of the interesting information. At weak coupling we show that the matrix model is close to the Gaussian matrix model and that the free-energy scales as N^2. At strong coupling we show that if the theory contains one adjoint hypermultiplet then the free-energy scales as N^3. We also find the expectation value of a supersymmetric Wilson loop that wraps the equator. We demonstrate how to extract the effective couplings and reproduce results of Seiberg. Finally, we compare to results for the six-dimensional (2,0) theory derived using the AdS/CFT correspondence. We show that by choosing the hypermultiplet mass such that the supersymmetry is enhanced to N=2, the Wilson loop result matches the analogous calculation using AdS/CFT. The free-energies differ by a rational fraction.