SLE, CFT and zig-zag probabilities

Details SLE, CFT and zig-zag probabilities SLE, CFT and zig-zag probabilities

2004-01-12

arxiv.org/abs/math-ph/0401019v1

Physics

Mathematical Physics

41 pages. Proceedings of the conference `Conformal Invariance and Random Spatial Processes', Edinburgh, July 2003

Scientific paper

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.

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