Spontaneous supersymmetry breaking in two dimensional lattice super QCD

TL;DR

This paper presents a non-perturbative lattice study of two-dimensional super QCD with exact supersymmetry, showing spontaneous supersymmetry breaking when the number of fermions is less than the gauge group rank.

Contribution

First numerical investigation of 2D super QCD on the lattice with exact supersymmetry, exploring spontaneous SUSY breaking in this toy model.

Findings

Evidence of spontaneous supersymmetry breaking when N_f < N_c

Lattice formulation preserves a single exact supersymmetry at finite lattice spacing

First non-perturbative insights into 2D super QCD with fundamental fermions

Abstract

We report on a non-perturbative study of two dimensional $\cN=(2,2)$ 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.