Conformal Field Theory for Multiple SLE

Abstract

Schramm-Loewner evolutions (SLEs) are the scaling limits of interface curves in planar statistical models, characterized by a conformal Markov property and Loewner’s growth process. Imposing alternating boundary conditions on the model leads to a collection of interface curves that interact with each other, the so-called multiple SLEs. In recent years much attention has been given to the characterization of all possible systems of multiple SLEs and deriving their properties. In this talk I will explain recent joint work with Nam-Gyu Kang (KIAS) and Nikolai Makarov (Caltech) that uses a Gaussian Free Field based Conformal Field Theory to analyze systems of multiple SLEs. In particular, we re-derive Dubedat’s commutation relations, generate an infinite family of martingale observables for the processes, and re-interpret Dubedat’s method of screening all within the framework of our CFT.