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

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).Comment: 18pages. To appear in J. Korean Math. So