The Coleman correspondence at the free fermion point.
Abstract: Two-dimensional statistical and quantum field theories are
special in many ways. One striking instance of this is the equivalence
of certain bosonic and fermionic fields, known as bosonization. I will
first review the idea of this correspondence in the explicit instance of
the massless Gaussian free field and massless Euclidean Dirac
fermions. I will then present a result that extends this
correspondence to the `massless' sine-Gordon field on $\R^2$ at
$\beta=4\pi$ and massive Dirac fermions. This is an instance of
Sidney Coleman's prediction that the `massless' sine-Gordon model and the massive Thirring model are equivalent. We use this correspondence to show that correlations of the `massless'
sine-Gordon model decay exponentially for $\beta=4\pi$. This is joint
work with C. Webb.