Conformal Field Theory on Multiply Connected Domains

Abstract

We implement a version of conformal field theory on a multiply connected domain. We show that all correlation functions for the Dirichlet Gaussian Free Field are martingale observables for a stochastic Loewner evolution on the domain. As part of it we derive the generalized Eguchi-Ooguri equations, which give an explicit form of Ward’s equations that describes the insertion of a stress tensor in terms of Lie derivatives and differential operators depending on the Teichmuller modular parameters. Joint work with Sung-Soo Byun and Nam-Gyu Kang.