$QCD_3$ Dualities and the F-Theorem

TL;DR

This paper investigates dualities in 2+1 dimensional QCD using the F-theorem, establishing bounds on parameter ranges for symmetry-breaking phases, with exact results for SU(2) and approximate for larger N.

Contribution

It provides the first bounds on the parameter space for symmetry-breaking phases in 2+1D QCD dualities, utilizing the F-theorem to constrain these phases.

Findings

Exact bounds for SU(2) gauge theory

Approximate bounds for SU(N) with N>2

Constraints on symmetry-breaking phases

Abstract

There has recently been a surge of new ideas and results for 2+1 dimensional gauge theories. We consider a recently proposed duality for 2+1 dimensional QCD, which predicts a symmetry-breaking phase. Using the F-theorem, we find bounds on the range of parameters for which the symmetry-breaking phase (and the corresponding duality) can occur. We find exact bounds for an $ SU(2) $ gauge theory, and approximate bounds for an $SU(N) $ gauge theory with $ N>2 $.