Deformations of the moduli space and superpotential flows in 3D SUSY QCD

We study the moduli space of three-dimensional $\mathcal{N}=2$ SQCD with $SU(N)$ gauge group and $F<N$ massless flavors. In the case of an $SU(2)$ theory with a single massless flavor, we explicitly calculate the quantum constraint $YM=1$ and generalize the calculation to models with arbitrary $N$ and $F=N-1$ flavors. In theories with $F<N-1$ flavors, we find that analogous constraints exist in locally defined coordinate charts of the moduli space. The existence of such constraints allows us to show that the Coulomb branch superpotential generated by single monopole effects is equivalent to the superpotential generated by multi-monopole contributions on the mixed Higgs-Coulomb branch. As a check for our result, we implement the local constraints as Lagrange multiplier terms in the superpotential and verify that deformations of a theory by a large holomorphic mass term for the matter fields results in a flow of the superpotential from the $F$-flavor model to the superpotential of an $(F-1)$-flavor model.