Large N expansion for superfluid Fermi gases at unitarity

We study an s-wave resonant Fermi gas near the unitarity point. We treat this problem by generalizing the Fermi gas to a model with $2N$ hyperfine states (with Sp($2N$) symmetry). We show that for $N=\infty$, the model can be solved exactly by the BEC-BCS mean field solution. In order to address the physically relevant problem ($N=1$), we perform a systematic $1/N$ loop expansion around the BEC-BCS solution. For $N=1$, we obtain a variety of thermodynamic quantities, including the energy, the pairing gap, and the upper critical polarization. We compare our results to experimental data and other theoretical approaches.