Infrared Stable Supersymmetry in Chern-Simons Theories with Matter and Quenched Disorder

Abstract

We study Abelian Chern-Simons field theories with matter fields and global $\mathrm{SU}(N)$ symmetry in the presence of random weak quenched disorder. In the absence of disorder, these theories possess $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ supersymmetric fixed points and $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ supersymmetric fixed lines in the infrared limit. We show that, although the presence of disorder forbids any supersymmetry of the bare action, infrared stable supersymmetric fixed points and fixed lines are realized in the disorder-averaged effective theories.