Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large- N behavior of 5-dimensional N $$ \mathcal{N} $$ = 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, λ ˜ $$ \tilde{\lambda} $$ ≡ 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 λ ˜ $$ \tilde{\lambda} $$ , although the details differ between small and large values of λ ˜ $$ \tilde{\lambda} $$ . For pure Chern-Simons theories we present evidence for a chain of phase transitions as λ ˜ $$ \tilde{\lambda} $$ is increased