Large $N$ theory of critical Fermi surfaces

Understand

We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions.

• The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces.
• We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$\Sigma$ path integral of the theory is expressed in terms of fields bilocal in spacetime.
• The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature.