Probability and Mathematical Physics Seminar

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We present recent progress on the massless sine-Gordon model at the free fermion point. In particular, we prove that the fractional charge (vertex operator) correlation functions exist, and they can be described by certain renormalised determinants of massive free fermions with branching. The latter were studied by Palmer, whose results combined with ours should yield explicit Hilbert-Schmidt determinant formulas for the correlation functions, and also imply predictions of Bernard-Leclair that the fractional two-point function satisfies a certain PDE.