Note on Schramm-Loewner Evolution for Superconformal Algebras

Abstract

Using the group-theoretical formulation of Schramm-Loewner evolution (SLE), we propose variants of SLE related to superconformal algebras. The corresponding stochastic differential equation is derived from a random process on an infinite-dimensional Lie group. We consider random processes on a certain kind of groups of superconformal transformations generated by exponentiated elements of the Grassmann envelop of the superconformal algebras. We present a method for obtaining local martingales from a representation of the superconformal algebra after integration over the Grassmann variables.