Supersymmetry in QCD$_2$ coupled to fermions

Abstract

We consider $1+1$ dimensional Yang-Mills theory with gauge group $G$ coupled to a massive Majorana fermion field in an adjoint representation and a number of massless Dirac or Majorana fermions transforming in arbitrary representations of the gauge group $G$. It is shown that the spectrum of the massive sector of this theory becomes supersymmetric at particular mass of adjoint fermion. This mass is independent of the detailed structure of the massless sector of the model and depends only on the gauge group $G$ and integer $k$ measuring the total anomaly. The massless sector of the model is shown to be not necessarily supersymmetric.