Supersymmetric gauge theories, Coulomb gases and Chern-Simons matrix models

Georgios Giasemidis, Richard J. Szabo, Miguel Tierz

Published 2013-10-11, updated 2013-10-22Version 2

We develop Coulomb gas pictures of strong and weak coupling regimes of supersymmetric Yang-Mills theory in five and four dimensions. By relating them to the matrix models that arise in Chern-Simons theory, we compute their free energies in the large N limit and establish relationships between the respective gauge theories. We use these correspondences to rederive the N^3 behaviour of the perturbative free energy of supersymmetric gauge theory on certain toric Sasaki-Einstein five-manifolds, and the one-loop thermal free energy of N=4 supersymmetric Yang-Mills theory on a spatial three-sphere.