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

Abstract

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.

17 pages; v2: reference added

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Cited by in corpus (4)

• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• Phases of five-dimensional supersymmetric gauge theories
• Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory