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

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

2005-11-16

arxiv.org/abs/math-ph/0511054v2

Commun.Math.Phys.268:687-716,2006

Physics

Mathematical Physics

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

Scientific paper

10.1007/s00220-006-0106-1

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.

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