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

TL;DR

This paper explores the dynamics and dualities of three-dimensional ${ m N}=1$ supersymmetric theories, revealing emergent symmetries, dual descriptions, and the structure of moduli spaces, with implications for supersymmetry enhancement and gauge theory behavior.

Contribution

It introduces new dualities and describes emergent symmetries in 3d ${ m N}=1$ theories, including a dual Wess-Zumino model with enhanced supersymmetry.

Findings

Emergent time reversal symmetry in certain theories.

Dual Wess-Zumino model with manifest $SU(3)$ symmetry.

Non-perturbative lifting of moduli space in ${ m N}=1$ $SU(N)$ gauge theories.

Abstract

We study the dynamics of certain 3d ${\cal N}=1$ 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 ${\cal N}=2$ $U(1)$ 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 ${\cal N}=1$ 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 ${\cal N}=1$ $SU(N)$ 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.