  We study the effective field theory of 2D fermions with a short-range
interaction in the presence of a van Hove singularity. We find that there are
additional divergences associated with the singularity that necessitate
regularization beyond the usual Wilsonian cut-off. In the full theory these
divergences are cut off by the finite size of the Brillouin zone. This leads to
a UV/IR mixing and causes the RG equation for the coupling constant to have an
explicit dependence on the ratio of the Wilsonian cut-off to the bandwidth. We
discuss the properties of the superconducting ground state and the transport
properties of the normal state and show that the latter are approximately
described by the marginal Fermi liquid scenario. To leading order, our results
are universal in the sense that they do not depend upon the nature of the
non-van Hove portion of the Fermi surface. We also comment on the van Hove
scenario of high-Tc superconductivity.
