Conformal field theory of dipolar SLE with the Dirichlet boundary condition

TL;DR

This paper develops a dipolar conformal field theory framework with Dirichlet boundary conditions, establishing martingale properties for certain fields and proving key properties of dipolar SLE processes.

Contribution

It introduces a new dipolar CFT approach with Dirichlet boundary conditions and proves martingale-observables and restriction properties for dipolar SLE.

Findings

Correlators are martingale-observables for dipolar SLE.

Proves the restriction property of dipolar SLE(8/3).

Establishes Friedrich-Werner's formula in the dipolar setting.

Abstract

We develop a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirichlet boundary condition and prove that correlators of certain family of fields in this theory are martingale-observables for dipolar SLE. We prove the restriction property of dipolar SLE(8/3) and Friedrich-Werner's formula in the dipolar case.