Algebraic properties of CFT coset construction and Schramm-Loewner evolution

TL;DR

This paper explores the algebraic properties of conformal field theory coset constructions and their relation to Schramm-Loewner evolution, extending SLE with Brownian motion on Lie groups to coset spaces and connecting to minimal models.

Contribution

It generalizes SLE with Brownian motion on Lie groups to coset spaces and investigates their connection to minimal models in conformal field theory.

Findings

Extended SLE to coset spaces G/A with Brownian motion.

Established links between SLE and coset models of CFT.

Provided conditions for minimal models within this framework.

Abstract

Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are martingales with respect to SLE. We generalize Schramm-Loewner evolution with additional Brownian motion on Lie group $G$ to the case of factor space $G/A$. We then study connection between SLE description of critical behavior with coset models of conformal field theory. In order to be consistent such construction should give minimal models for certain choice of groups.