Towards a conformal field theory for Schramm-Loewner evolutions

TL;DR

This paper explores the connection between Schramm-Loewner evolutions and conformal field theory, focusing on partition functions and correlation functions to understand critical phenomena in 2D statistical mechanics.

Contribution

It provides a comprehensive analysis of the relationship between SLE and CFT, offering new insights and perspectives on their interplay and remaining challenges.

Findings

Linking SLE partition functions with CFT correlation functions

Identifying difficulties in establishing a rigorous connection

Suggesting future research directions in the field

Abstract

We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in critical models in two-dimensional statistical mechanics. We gather and supplement previous results with different perspectives, point out remaining difficulties, and suggest directions for future studies.