Annulus SLE partition functions and martingale-observables

Sung-Soo Byun (Seoul National University), October 11, 2018

Abstract: In this talk, I will introduce a version of conformal field theory (CFT) and explain its implementations to SLE theory in a doubly connected domain. The basic fields in these implementations are one-parameter family of Gaussian free fields whose boundary conditions are given by a weighted combination of Dirichlet boundary condition and excursion-reflected one. After explaining basic notions in CFT such as OPE families of central charge modifications of the Gaussian free field and presenting certain equations including a version of Eguchi-Ooguri and Ward’s equations, I will outline the relation between CFT and SLE theory. As an application, I will explain how to apply the method of screening to find Euler integral type solutions to the parabolic partial differential equations for the annulus SLE partition functions introduced by Zhan and present a class of SLE martingale-observables associated with these solutions. This is based on joint work with Nam-Gyu Kang and Hee-Joon Tak.