Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large-N behavior of 5-dimensional N = 1 super Yang-Mills with a level k Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as N-5/2 for U(N) gauge groups with large values of the Chern-Simons 't Hooft coupling, (lambda) over tilde = N/k. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the N-5/2 behavior parallels other fixed points which have known supergravity duals. We also demonstrate that SU(N) gauge groups cannot have this N-5/2 scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of (lambda) over tilde, although the details differ between small and large values of (lambda) over tilde. For pure Chern-Simons theories we present evidence for a chain of phase transitions as (lambda) over tilde is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamentalWilson loops. Different choices of the integration contours also lead to different properties for the loops.