Singular corrections to the Fermi-liquid theory

We show that the singularities in the dynamical bosonic response functions of a two-dimensional Fermi liquid give rise to universal nonanalytic corrections to the results of the Fermi-liquid theory. In particular, we find a T-2 term in the specific heat, linear-in-T terms in the effective mass and in the uniform spin susceptibility chi(s)(Q=0,T), and \Q\ term in chi(s)(Q,T=0). The existence of these terms has been the subject of recent controversy, which is resolved in this paper. We present exact expressions for all nonanalytic terms to second order in a generic interaction U(Q) and show that the nonanalytic terms originate exclusively from forward- and backward-scattering of particles with zero total momentum.