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 T² term in the specific heat, linear-in-T terms in the effective mass and in the uniform spin susceptibility χ_s(Q = 0, T), and |Q| term in χ_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.