  We study the Kohn-Luttinger effect in a two-dimensional (2D) nested Fermion
liquid with a repulsive interaction via the renormalization group method and
identify the resulting order parameter symmetry. Using the band structure of
the 2D Hubbard model close to half-filling as a prototype, we construct an
effective low-energy theory. We use multidimensional bosonization to
incorporate the zero-sound channel and find marginal Fermi liquid behavior in
the absence of any instability. We show an analog of the Landau theorem in
nested Fermion liquids, which serves as the criterion of the BCS instability.
Including repulsive or antiferromagnetic exchange interactions in the
low-energy theory, we show that the $d_{x^2-y^2}$-wave BCS channel is
renormalized to be the most attractive. Below half-filling, when the nesting is
not perfect, there is competition between the spin-density-wave (SDW) and the
BCS channels; when the SDW coupling is small enough, there occurs a
$d_{x^2-y^2}$-wave superconducting instability at sufficiently low
temperatures.
