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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 quantumconstraint $YM=1$ and generalize the calculation to models with arbitrary $N$and $F=N-1$ flavors. In theories with $F<N-1$ flavors, we find that analogousconstraints exist in locally defined coordinate charts of the moduli space. Theexistence of such constraints allows us to show that the Coulomb branchsuperpotential generated by single monopole effects is equivalent to thesuperpotential generated by multi-monopole contributions on the mixedHiggs-Coulomb branch. As a check for our result, we implement the localconstraints as Lagrange multiplier terms in the superpotential and verify thatdeformations of a theory by a large holomorphic mass term for the matter fieldsresults in a flow of the superpotential from the $F$-flavor model to thesuperpotential of an $(F-1)$-flavor model.

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