  We study 2D fermions with a short-range interaction in the presence of a van
Hove singularity. It is shown that this system can be consistently described by
an effective field theory whose Fermi surface is subdivided into regions as
defined by a factorization scale, and that the theory is renormalizable in the
sense that all of the counterterms are well defined in the IR limit. The theory
has the unusual feature that the renormalization group equation for the
coupling has an explicit dependence on the renormalization scale, much as in
theories of Wilson lines. In contrast to the case of a round Fermi surface,
there are multiple marginal interactions with nontrivial RG flow. The Cooper
instability remains strongest in the BCS channel. We also show that the
marginal Fermi liquid scenario for the quasiparticle width is a robust
consequence of the van Hove singularity. Our results are universal in the sense
that they do not depend on the detailed properties of the Fermi surface away
from the singularity.

Strongly Correlated Electrons;High Energy Physics - Theory