Coupling of Gaussian free field with general slit SLE

Alexey Tochin, Alexander Vasil'ev

Published 2015-06-23Version 1

We consider the coupling between the Gaussian free field and the slit holomorphic stochastic flow, called ($\delta,\sigma$)-SLE, which contains known SLE processes (chordal, radial, and dipolar) as particular cases. In physical terms, we study a free boundary conformal field theory with one scalar bosonic field, where Green's function is assumed to have some general regular harmonic part. We establish which of these models allow a coupling with ($\delta,\sigma$)-SLE, or equivalently, when the correlation functions induce the local ($\delta,\sigma$)-SLE martingales (martingale observables).