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

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 κ = 8/3, which corresponds to the central charge c = 0 and the case when loops are suppressed in the corresponding O(n) model.