Conformal field theory of dipolar SLE(4) with mixed boundary condition

TL;DR

This paper develops a dipolar conformal field theory with mixed boundary conditions and demonstrates that certain correlation functions serve as martingale-observables for dipolar SLE(4), linking CFT and stochastic processes.

Contribution

It introduces a new dipolar CFT framework with Dirichlet-Neumann boundary conditions and establishes its connection to dipolar SLE(4) martingale-observables.

Findings

Correlation functions are martingale-observables for dipolar SLE(4).

The developed theory applies to domains with mixed boundary conditions.

Central charge of the theory is one.

Abstract

We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condition and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian free field with a certain boundary value are martingale-observables for dipolar SLE(4).