Abstract
We study the large N phase diagram of an asymptotically free UV completion of mathcal{N} = 1 SU(N) super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling. We compute the effective superpotential at small gauge coupling λ ≡ N/k, and combine this with previous results in the literature to obtain the full phase diagram in this regime. We find that tuning the UV parameters allows us to reach various phases and fixed points of Chern-Simons theory that were recently discovered using large N techniques, as well as new phases that characterize the Yang-Mills theory. We also conjecture the form of the phase diagram for general values of λ and for finite N.
Highlights
Supersymmetry (SUSY) has proven to be an invaluable tool for studying quantum field theories (QFTs)
We study the large N phase diagram of an asymptotically free UV completion of N = 1 SU(N ) super-Yang-Mills-Chern-Simons theory coupled to a single massive fundamental scalar multiplet with a quartic superpotential coupling
This is in contrast to the line μ = 0, where there is no jump in the Witten index; there, vacua merge at a finite distance in parameter space and we find a second-order phase transition
Summary
Supersymmetry (SUSY) has proven to be an invaluable tool for studying quantum field theories (QFTs). In the limit ω = 0 [1] In this case the phase diagram was computed by calculating the 1-loop effective superpotential in the “Higgsed” phase for the theory (1.1). At leading order in small λ we can compute the full phase diagram, which appears in figure 5 This is the main result of this paper. We discuss possible extensions of this phase diagram to the strongly-coupled regions where λ is not necessarily small, and large but finite values of N. This analysis solves some puzzles that appear when considering the previous results more carefully.
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