Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs

Abstract

We study the dynamics of certain 3d $\mathcal{N}=1$ time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared and there exists (nonetheless) an exact moduli space of vacua. This theory has a dual description with manifest time reversal symmetry. Second, we consider some surprising facts about $\mathcal{N}=2$ $U(1)$ gauge theory coupled to two chiral superfields of charge 1. This theory is claimed to have emergent $SU(3)$ global symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a theory of scalars and fermions but no gauge fields) with manifest $SU(3)$ symmetry but only $\mathcal{N}=1$ supersymmetry. We argue that this Wess-Zumino model must have enhanced supersymmetry in the infrared. Finally, we make some brief comments about the dynamics of $\mathcal{N}=1$ $SU(N)$ gauge theory coupled to $N_f$ quarks in a time reversal invariant fashion. We argue that for $N_f<N$ there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted.

30 pages, 4 figures v2: references added

References in corpus (7)

• Generalized Global Symmetries
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Phases Of Adjoint QCD${}_3$ And Dualities
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Topological Model for Domain Walls in (Super-)Yang-Mills Theories
• Phases of $\mathcal{N}=1$ Theories in 2+1 Dimensions
• Smallest 3d hyperbolic manifolds via simple 3d theories

Cited by in corpus (34)

• Three-dimensional gauge theories with supersymmetry enhancement
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• M-theoretic Genesis of Topological Phases
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• A tale of exceptional 3d dualities
• Large N Renormalization Group Flows in 3d $\mathcal{N}=1$ Chern-Simons-Matter Theories
• Dualities and Phases of 3D N=1 SQCD
• Exceptional Chern-Simons-Matter Dualities
• Living on the walls of super-QCD
• Supersymmetric Indices of 3d S-fold SCFTs
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Seeking SUSY fixed points in the $4-\epsilon$ expansion
• Infrared enhancement of supersymmetry in four dimensions
• Chiral 3d SU(3) SQCD and N=2 mirror duality
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Flowing from 16 to 32 Supercharges
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• A supersymmetric SYK model with a curious low energy behavior
• Infrared phases of 3D Class R theories
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• 3D Dualities and Supersymmetry Enhancement from Domain Walls
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Five loop renormalization of the Wess-Zumino model
• Global Aspects of Spaces of Vacua
• Phases of $\mathcal{N}=1$ Quivers in $2+1$ Dimensions
• Generalized Euler Index, Holonomy Saddles, and Wall-Crossing
• Full Phase Diagram of a UV Completed $\mathcal{N}=1$ Yang-Mills-Chern-Simons Matter Theory
• Emergent Supersymmetry at Large $N$
• Mildly Flavoring Domain Walls in Sp(N) SQCD
• Sequential deconfinement in $3d$ $\mathcal{N}=2$ gauge theories
• Critical properties of three-dimensional many-flavour QEDs
• Aspects of 4d supersymmetric dynamics and geometry