Coupling of Gaussian free field with general slit SLE

Abstract

We consider a coupling of the Gaussian free field with slit holomorphic stochastic flows, 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 coupling with ($\delta,\sigma$)-SLE, or equivalently, when the correlation functions induce local ($\delta,\sigma$)-SLE martingales (martingale observables).