Aspects of Ising-nematic quantum critical point

We devise a renormalization group analysis for quantum field theories
with Fermi surface to study scaling behaviour of non-Fermi liquid
states in a controlled approximation. The non-Fermi liquid fixed
points are identified from a Fermi surface in (m+1) spatial
dimensions, while the co-dimension of Fermi surface is also extended
to a generic value. We also study superconducting instability in such
systems as a function of dimension and co-dimension of the Fermi
surface. The key point in this whole analysis is that unlike in
relativistic QFT, the Fermi momentum $k_F$ enters as a dimensionful
parameter, thus modifying the naive scaling arguments. The effective
coupling constants are found to be combinations of the original
coupling constants and $k_F$.