Coupling of Gaussian free field with general slit SLE

TL;DR

This paper explores the coupling between Gaussian free fields and a broad class of slit SLE processes, extending known models and identifying conditions for their interaction within conformal field theory.

Contribution

It introduces the ($oldsymbol{ ext{} ext{ extbf{δ,σ}}}$)-SLE framework and determines when it can be coupled with Gaussian free fields, generalizing existing SLE models.

Findings

Identifies conditions for coupling Gaussian free fields with ($oldsymbol{ ext{} ext{ extbf{δ,σ}}}$)-SLE.

Extends known SLE processes as special cases within the ($oldsymbol{ ext{} ext{ extbf{δ,σ}}}$)-SLE framework.

Provides criteria for when correlation functions induce local martingales for these processes.

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).