On Stochastic Evolutions and Superconformal Field Theory

TL;DR

This paper explores the extension of stochastic evolutions of superconformal maps to the Ramond sector and examines how different superconformal structures influence their connection to superconformal field theory.

Contribution

It extends the known links between stochastic superconformal maps and superconformal field theory to the Ramond sector and analyzes effects of alternative superconformal structures.

Findings

Extended stochastic evolutions to the Ramond sector.

Analyzed modifications with unconventional superconformal structures.

Connected superconformal maps to singular vectors in superconformal algebra.

Abstract

Links between certain stochastic evolutions of conformal maps and conformal field theory have been studied in the realm of SLE and by utilizing singular vectors in highest-weight modules of the Virasoro algebra. It was recently found that this scenario could be extended to stochastic evolutions of 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. Here we discuss the analogous extension to the Ramond sector. We also discuss how the links are modified when an unconventional superconformal structure or superderivative is employed.