$\mathcal{N}{=}1$ dualities in 2+1 dimensions

TL;DR

This paper proposes a new duality in 2+1 dimensional supersymmetric QCD involving $SU(N)$ and $U(k)$ gauge groups, with consistency checks aligning it with known dualities like 3d bosonization and 4d Seiberg duality.

Contribution

It introduces an infrared duality between $SU(N)$ and $U(k)$ gauge theories with supersymmetry, supported by vacuum structure analysis and perturbative calculations.

Findings

Duality connects $SU(N)$ and $U(k)$ gauge theories in 3d supersymmetric QCD.

Vacuum structure mapping supports the duality proposal.

Perturbative checks in the $oldsymbol{ ext{epsilon}}$-expansion validate the duality.

Abstract

We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) \leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $\varepsilon$-expansion.