Duality and Confinement in 3d $\mathcal{N}=2$ "chiral" $SU(N)$ gauge theories

TL;DR

This paper explores the rich quantum structure, dualities, and confinement phases of 3d $ abla$ 2$ SU(N)$ gauge theories with chiral matter, revealing novel dualities and supersymmetry breaking scenarios.

Contribution

It proposes new dualities and confinement phases for 3d $ abla$ 2$ SU(N)$ theories with chiral matter, including a novel duality between $SU(N)$ and $USp(2\tilde{N})$ theories.

Findings

Many Coulomb branch operators remain massless and are mapped under dualities.

Certain theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking.

Multiple dual descriptions exist for specific $SU(2)$ gauge theories with $2F$ doublets.

Abstract

We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between $SU(N)$ and $USp(2 \tilde{N})$ theories. For the 3d $\mathcal{N}=2$ $SU(2)$ gauge theory with $2F$ doublets, there are generally $F+2$ "chiral" and "non-chiral" dual descriptions.