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

TL;DR

This work extends the landscape of 3d dualities by proposing IR ${\mathcal{N}}=1$ SU(N) ⇄ U(k) dualities with Chern-Simons terms and cubic superpotentials, supplemented by gauge-singlet fields on one side. It builds a concrete operator dictionary (e.g., mesons to singlets, monopoles to baryons) and checks consistency through vacuum matching under mass deformations and perturbative ${\varepsilon}$-expansion, linking to both 3d bosonization and 4d Seiberg duality. The analysis covers Abelian and non-Abelian cases, derives several dual pairs (including ${SU/U}$, ${U/SU}$, and ${U/U}$), and lays out a natural path to generalize to ${N_f>1}$ flavors. The results provide a SUSY-based framework for exploring 2+1d dualities with limited supersymmetry, with potential connections to non-SUSY dualities and brane constructions, and potential implications for understanding IR phases in strongly coupled gauge theories.

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.