Universal Planar Abelian Duals for 3d $\mathcal{N}=2$ Unitary CS-SQCD

TL;DR

This paper constructs a universal planar Abelian dual for 3d $ ext{N}=2$ $U(N)_k$ SQCD theories, covering all parameters where supersymmetry remains unbroken, thus unifying various dualities into a comprehensive framework.

Contribution

It introduces a systematic algorithm to derive a universal planar Abelian dual for 3d $ ext{N}=2$ $U(N)_k$ SQCD across the entire parameter space, extending previous limited dualities.

Findings

Unified dual description valid for all parameters with unbroken supersymmetry.

Systematic method to track dual flows under mass deformations.

Generalization of chiral-planar dualities beyond specific loci.

Abstract

We provide an explicit planar Abelian dual for three-dimensional $\mathcal{N}=2$ $U(N)_k$ SQCD with $F$ fundamental chiral multiplets. This construction covers the entire $(N, F, k)$ parameter space (provided supersymmetry is unbroken), offering a unified framework for the infrared physics of these theories. Our results generalize a recently discovered class of chiral-planar dualities, which were previously limited to the locus $F = 2|k| + 2N$, which is a mass deformation of $\mathcal{N}=4$ mirror symmetry plus a restricted set of additional mass deformations. By developing a systematic algorithm to track the flow of the dual theory under generic mass deformations, we establish the planar Abelian quiver not merely as a specific dual description, but as a universal tool for analyzing 3d gauge dynamics.