Supersymmetric Color Superconductivity

Recent interest in novel phases in high density QCD motivates the study ofhigh density supersymmetric QCD (SQCD), where powerful exact results forsupersymmetric gauge theories can be brought to bear in the strongly coupledregime. We begin by describing how a chemical potential can be incorporatedinto a supersymmetric theory as a spurion vector superfield. We then studysupersymmetric SU(N_c) gauge theories with N_f flavors of quarks in thepresence of a baryon chemical potential mu, and describe the global symmetrybreaking patterns at low energy. Our analysis requires mu < Lambda and is thuscomplementary to the variational approach that has been successful for mu < mu_c. Wealso give a qualitative description of the phases in the `conformal window',3/2 N_c < N_f < 3N_c, at finite density.Comment: 29 pages, LaTe