This article is cited in 1 paper

Note on Schramm–Loewner evolution for superconformal algebras

S. Koshida

Department of Basic Science, University of Tokyo, Tokyo, Japan

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.

Keywords: Schramm–Loewner evolution, conformal field theory, superconformal algebra.

Received: 25.06.2018
Revised: 25.06.2018

DOI: 10.4213/tmf9598

 English version: Theoretical and Mathematical Physics, 2019, 199:1, 501–512

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