A Chiral-Planar dualization algorithm for 3d $\mathcal{N}=2$ Chern-Simons-matter theories

TL;DR

This paper introduces an algorithm to systematically find abelian planar dual descriptions of a broad class of 3d $ abla=2$ chiral Chern-Simons gauge theories, enhancing understanding of their dualities.

Contribution

The authors develop a mirror dualization algorithm that simplifies deriving abelian-planar duals for chiral quivers from known $ abla=4$ mirror pairs, using real mass deformations.

Findings

The algorithm effectively identifies dual vacua despite Coulomb branch complexity.

It applies to a broad class of chiral Chern-Simons theories.

Systematic derivation of dual descriptions is achieved.

Abstract

We show that a broad class of three-dimensional $\mathcal{N}=2$ chiral Chern-Simons gauge theories admit an abelian and planar dual description. These chiral-planar dualities emerge by performing real mass deformations on known $\mathcal{N}=4$ mirror pairs, using the $\mathcal{N}=2^*$ setup to flow to chiral theories on the electric side. While identifying the correct dual vacuum is subtle due to the rich structure of the Coulomb branch, we develop a mirror dualization algorithm that streamlines this process and systematically provides the abelian-planar duals of chiral quivers.