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

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.

32 pages. v2: section 5.2 removed, version accepted for publication in Commun. Math. Phys

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• Twenty-five years of two-dimensional rational conformal field theory
• Towards a conformal field theory for Schramm-Loewner evolutions
• Calculus on manifolds of conformal maps and CFT
• Random loops and conformal field theory
• Hypotrochoids in conformal restriction systems and Virasoro descendants
• The Brownian loop soup stress-energy tensor
• Three Dimensional Gravity and Schramm-Loewner Evolution