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 Nf quarks in a time reversal invariant fashion. We argue that for Nf< N there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted.