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

## TL;DR

This paper investigates the structure of the moduli space and superpotential flows in 3D $ ext{SU}(N)$ supersymmetric QCD with fewer flavors, deriving quantum constraints and analyzing monopole contributions to the superpotential.

## Contribution

It explicitly calculates quantum constraints in 3D $ ext{SU}(N)$ SQCD with various flavors and demonstrates the equivalence of monopole-generated superpotentials, extending understanding of moduli space deformations.

## Key findings

- Quantum constraint $YM=1$ for $SU(2)$ with one flavor.
- Existence of local constraints in theories with fewer flavors.
- Superpotential flow from $F$ to $F-1$ flavors via mass deformation.

## Abstract

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.