Exact Renormalisation Group and pairing in many-fermion systems

We consider pairing phenomena in the framework of the exact renormalisation group. We introduce a boson field to describe pairing effects, and take a simple ansatz for the effective action. We derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The initial conditions are obtained by renor- malising the interaction to fit the scattering length in vacuum. At some critical value of the running scale, the numerical solutions show a phase transition to a gapped phase. Standard results are recovered if we omit the boson loops.