Conformal restriction, highest-weight representations and SLE

TL;DR

This paper establishes a connection between Schramm-Loewner Evolutions (SLE) and highest-weight representations of infinite-dimensional Lie algebras, confirming predictions from conformal field theory about 2D critical systems.

Contribution

It demonstrates how to relate SLE to highest-weight representations using conformal restriction, bridging probability theory and algebraic structures in physics.

Findings

SLE can be described via highest-weight representations

Confirms the link between 2D critical systems and degenerate representations

Provides a mathematical framework connecting SLE and conformal field theory

Abstract

We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite dimensional Lie Algebras using the conformal restriction properties studied by Lawler, Schramm and Werner in the paper arXiv:math.PR/0209343. This confirms the prediction from theoretical physics and conformal field theory that two-dimensional critical systems are related to such degenerate representations.