Identification of the stress-energy tensor through conformal restriction in SLE and related processes

TL;DR

This paper establishes a connection between Schramm-Loewner Evolution (SLE) at kappa=8/3 and conformal field theory by deriving Ward identities and identifying probabilities with stress-energy tensor correlation functions, highlighting a specific case where loops are suppressed.

Contribution

It derives Ward identities for SLE at kappa=8/3 using conformal restriction, linking SLE probabilities to CFT stress-energy tensor correlations.

Findings

Derived Ward identities for SLE at kappa=8/3

Connected SLE probabilities with stress-energy tensor correlations

Applicable to loop-suppressed models with central charge c=0

Abstract

We derive the Ward identities of Conformal Field Theory (CFT) within the framework of Schramm-Loewner Evolution (SLE) and some related processes. This result, inspired by the observation that particular events of SLE have the correct physical spin and scaling dimension, and proved through the conformal restriction property, leads to the identification of some probabilities with correlation functions involving the bulk stress-energy tensor. Being based on conformal restriction, the derivation holds for SLE only at the value kappa=8/3, which corresponds to the central charge c=0 and the case when loops are suppressed in the corresponding O(n) model.