Polarized fermions in the unitarity limit

We consider a polarized Fermi gas in the unitarity limit. Results are calculated analytically up to next-to-leading order in an expansion about d=4 spatial dimensions. We find a first order transition from superfluid to normal phase. The critical chemical potential asymmetry for this phase transition is delta_mu_c= 2/(mu epsilon)*(1-0.467\epsilon), where epsilon=4-d is the expansion parameter and 'mu' is the average chemical potential of the two fermion species. Stability of the superfluid phase in the presence of supercurrents is also studied.