On conformal field theory of SLE(kappa; rho)

TL;DR

This paper explores the conformal field theory perspective of SLE(kappa; rho), linking it to statistical mechanics, martingales, and Coulomb gas formalism, and proposes a potential generalization of the process.

Contribution

It provides a CFT interpretation of SLE(kappa; rho) as boundary interfaces created by vertex operators, and shows certain correlation function ratios are martingales.

Findings

Ratios of CFT correlation functions are martingales.

SLE(kappa; rho) describes interfaces with boundary conditions from Coulomb gas formalism.

Partition functions have a simple product form due to total charge neutrality.

Abstract

SLE(kappa; rho), a generalization of chordal Schramm-L\"owner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(kappa; rho) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges alpha = rho/(2 sqrt(kappa)). The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(kappa; rho).