SLE, CFT and zig-zag probabilities
Mathematical Physics
2007-05-23 v1 Statistical Mechanics
High Energy Physics - Theory
math.MP
Probability
Abstract
The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or annular SLEs. Second, we review the main features of our approach connecting SLEs to conformal field theories (CFTs). It is based on using boundary CFTs to probe the SLE hulls. Finally, we study zig-zag probabilities and their relation with CFT correlation functions. We suggest a putative link between the braiding of SLE samples and that of CFT correlation functions.
Cite
@article{arxiv.math-ph/0401019,
title = {SLE, CFT and zig-zag probabilities},
author = {Michel Bauer and Denis Bernard},
journal= {arXiv preprint arXiv:math-ph/0401019},
year = {2007}
}
Comments
41 pages. Proceedings of the conference `Conformal Invariance and Random Spatial Processes', Edinburgh, July 2003