#### 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.