  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.
