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Global well-posedness of the dynamical sine-Gordon model up to $6\pi$
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abstract
We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters $\beta^2 < 6\pi$. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely deterministic and completely captures the size of the solution to the dynamical sine-Gordon model. The probabilistic fluctuations in the dynamical sine-Gordon model are then controlled using uniform estimates for modified stochastic objects.
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Twisted Dirac operators and fractional correlations of the massless sine-Gordon model at the free fermion point
Fractional vertex-operator correlations of the massless sine-Gordon model at β = 4π are shown to equal Palmer's tau functions of massive twisted Dirac operators, giving a proof of the Lukyanov-Zamolodchikov one-point formula.
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