Exact renormalization group flow for ultracold Fermi gases in the unitary limit

We study the exact renormalization group flow for ultracold Fermi gases in the unitary regime. We introduce a pairing field to describe the formation of the Cooper pairs and take a simple ansatz for the effective action. A set of approximate flow equations for effective couplings including boson and fermionic fluctuations is derived. At some value of the running scale, the system undergoes a phase transition to a gapped phase. The values of the energy density, chemical potential, pairing gap and the corresponding proportionality constants relating the interacting and non-interacting Fermi gases are calculated. Standard mean-field results are recovered if we omit the boson loops.