Dualities and Phases of 3D N=1 SQCD

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.

45 pages, 7 figures

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• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Exceptional Chern-Simons-Matter Dualities
• Living on the walls of super-QCD
• Chiral 3d SU(3) SQCD and N=2 mirror duality
• Thermal order in large N conformal gauge theories
• Generalized Giveon-Kutasov duality
• 3d $\mathcal{N}=2$ dualities for $SU(N_c)\times U(1)$ Chern-Simons gauge theories
• 3D Dualities and Supersymmetry Enhancement from Domain Walls
• Dualities of Adjoint QCD${}_3$ from Branes
• Phases of $\mathcal{N}=1$ Quivers in $2+1$ Dimensions
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities
• Global Aspects of Spaces of Vacua
• Dualities of 3D $\mathcal{N}=1$ SQCD from Branes and non-SUSY deformations
• Full Phase Diagram of a UV Completed $\mathcal{N}=1$ Yang-Mills-Chern-Simons Matter Theory
• Generalized Euler Index, Holonomy Saddles, and Wall-Crossing
• Sequential deconfinement in $3d$ $\mathcal{N}=2$ gauge theories
• Mildly Flavoring Domain Walls in Sp(N) SQCD
• Phases of QCD${}_3$ with three families of fundamental flavors
• Aspects of 4d supersymmetric dynamics and geometry