Abstract

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 $k_F$.