Supersymmetric Color Superconductivity

Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N_c) gauge theories with N_f flavors of quarks in the presence of a baryon chemical potential mu, and describe the global symmetry breaking patterns at low energy. Our analysis requires mu < Lambda and is thus complementary to the variational approach that has been successful for mu << Lambda. We find that for N_f < N_c a modified U(1)_B symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N_f=N_c there is a critical chemical potential above which the U(1)_B is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N_c+1 <= N_f < 3/2 N_c and find that baryon number is broken dynamically for mu > mu_c. We also give a qualitative description of the phases in the `conformal window', 3/2 N_c < N_f < 3N_c, at finite density.