Dualities and Phases of 3D N=1 SQCD

TL;DR

This work analyzes 3d N=1 SUSY gauge theories with matter, deriving a universal 1-loop effective superpotential and showing that the resulting phase diagrams for fundamental matter are group-independent. It demonstrates that the phase structure has a universal three-region form with a single phase transition at m_*, and uses symmetry arguments to prove this persists to all orders. Leveraging these results, the authors propose a web of N=1 dualities among U(N), SU(N), SO(N), and Sp(N) gauge theories, many linked to known N=2 dualities, and reveal emergent symmetries and potential exact moduli spaces in the IR. The study also connects to RG flows at large CS level, showing emergent supersymmetry in certain degenerate limits and providing a framework that potentially informs non-SUSY dualities via flow from N=2 to N=1 to non-SUSY regimes.

Abstract

We study gauge theories with N=1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for N=1 gauge theories with fundamental matter. We also show that these dualities are related to results in N=2 supersymmetric gauge theories, which provides further evidence for them.

Figures (7)

• Figure 1: Schematic general form of the phase diagram for the $\mathcal{N}=1$ gauge theories with CS terms and $N_f$ fundamental matter fields discussed in this paper. The blue graphs depict the effective potential. There are two semiclassical phases for large $|m|$, and an intermediate phase with $\min(N+1,N_f+1)$ solutions to the F-term equations with various symmetry breaking patterns. A similar phase diagram exists for $SO(N)$ and $Sp(N)$ gauge groups. The phase transition at $m=m_*$ is highly unnatural, since at this point many solutions of the F-term equations collide simultaneously. Nonetheless, this picture is an exact result to all orders in perturbation theory.
• Figure 2: Phase diagram for an $\mathcal{N}=1$$U(N)_{k+\frac{N+1}{2},{k+\frac{1}{2}}}$ gauge theory coupled to a single fundamental matter multiplet.
• Figure 3: The 1-loop diagrams we sum over for the 1-loop superpotential
• Figure 4: Phase diagram for an $\mathcal{N}=1$$U(1)_{k+\frac{N_f}{2}}$ gauge theory coupled to $N_f$ charge 1 matter multiplets.
• Figure 5: Phase diagram for an $\mathcal{N}=1$$SU(N)_{k+\frac{1}{2} N,k}$ gauge theory coupled to a $N_f$ fundamental matter multiplets. The precise form of the low-energy theories in the intermediate phase is discussed in the text.