Non-Abelian strings in a dense matter

We consider gauge theories with scalar matter with and without supersymmetry at nonzero chemical potential. It is argued that a chemical potential plays a role similar to the Fayet-Iliopoulos term. We analyze theory at the weak coupling regime at large chemical potential and argue that it supports non-Abelian non-Bogomol'nyi-Prasad-Sommerfield strings. World sheet theory on the non-Abelian string in a dense matter is briefly discussed