Conformal field theories in random domains and stochastic Loewner evolutions

TL;DR

This paper reviews the connection between conformal field theories and stochastic Loewner evolutions, highlighting how random conformal maps are integrated into the algebraic framework of CFTs.

Contribution

It introduces a unified perspective linking algebraic CFTs with probabilistic SLE methods through random conformal maps.

Findings

Establishes a relation between algebraic CFT and SLE.

Demonstrates the implementation of random conformal maps in CFT.

Provides insights into probabilistic approaches to conformal invariance.

Abstract

We review the recently developed relation between the traditional algebraic approach to conformal field theories and the more recent probabilistic approach based on stochastic Loewner evolutions. It is based on implementing random conformal maps in conformal field theories.