Matrix models for 5d super Yang–Mills**This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed Pestun and Zabzine) which contains 17 chapters available at [

Abstract

In this contribution to the issue on localization in gauge theories we investigate the matrix models derived from localizing super Yang–Mills on S5. 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 N2. At strong coupling we show that if the theory contains one adjoint hypermultiplet then the free-energy scales as N3. 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 , the Wilson loop result matches the analogous calculation using AdS/CFT. The free-energies differ by a rational fraction.