Rigorous proof of Fermi liquid behavior for jellium two-dimensional interacting fermions

Using the method of continuous constructive renormalization group around the Fermi surface, we prove that a jellium two-dimensional interacting system of fermions at low temperature T is analytic in the coupling constant lambda for \lambda\ \logT\ less than or equal to K, where K is some numerical constant and T is the temperature. In that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior seen in Fermi liquids but, in particular, not in Luttinger liquids. Our results also prove that in 2D any transition temperature must be nonperturbative in the coupling constant, a result expected on physical grounds. The proof exploits specific momentum conservation rules in two dimensions.