Stochastic evolutions in superspace and superconformal field theory

TL;DR

This paper explores how stochastic processes in superconformal maps relate to superconformal field theory, extending the connection between stochastic Loewner evolution and conformal field theory to supersymmetric contexts.

Contribution

It introduces a framework linking stochastic evolutions in N=1 superspace with superconformal field theory and superconformal algebra singular vectors.

Findings

Extended SLE to N=1 superspace

Linked stochastic maps to superconformal algebra

Identified superconformal singular vectors in stochastic context

Abstract

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu-Schwarz sector.