Spontaneous supersymmetry breaking in two dimensional lattice super QCD

We report on a non-perturbative study of two dimensional N = 2 2 $$ \mathcal{N}=\left(2,2\right) $$ super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U( N c ) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. We present evidence that the exact supersymmetry breaks spontaneously when N f < N c in agreement with theoretical expectations