Abstract
In this paper we investigate the large-N behavior of 5-dimensional \( \mathcal{N} \) = 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, \( \tilde{\lambda} \) ≡ 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 \( \tilde{\lambda} \), although the details differ between small and large values of \( \tilde{\lambda} \). For pure Chern-Simons theories we present evidence for a chain of phase transitions as \( \tilde{\lambda} \) 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-fundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops.
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Minahan, J.A., Nedelin, A. Phases of planar 5-dimensional supersymmetric Chern-Simons theory. J. High Energ. Phys. 2014, 49 (2014). https://doi.org/10.1007/JHEP12(2014)049
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DOI: https://doi.org/10.1007/JHEP12(2014)049