$QC{D}_3$ Dualities and the F-Theorem

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 $N>2$.