Abstract: This talk will be about a model that illustrates that statistical mechanics and field theory can be quite special in two dimensions -- even without conformal invariance. More precisely, I will discuss a special case of a prediction of S. Coleman which identifies correlation functions of the massless sine-Gordon model (with suitably chosen parameters) and massive free fermions. This is an instance of bosonization: a (interacting) bosonic field theory is expressed in terms of a (non-interacting) fermionic model. It also demonstrates that despite being a non-trivial (and non-conformal) field theory, the sine-Gordon model at the free fermion point remains integrable (correlation functions are explicit). As a consequence we also obtain exponential decay of correlations for the massless sine-Gordon model at the free fermion point.

This is joint work with Roland Bauerschmidt (Cambdridge): https://arxiv.org/pdf/2010.07096.pdf