On Conformal Field Theory and Stochastic Loewner Evolution

Details On Conformal Field Theory and Stochastic Loewner Evolution On Conformal Field Theory and Stochastic Loewner Evolution

2003-08-04

arxiv.org/abs/hep-th/0308020v2

Nucl.Phys. B687 (2004) 279-302

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 4 figures, LaTeX; v2: added section 4.1, references and minor clarifications, version to appear in NPB

Scientific paper

10.1016/j.nuclphysb.2004.03.025

We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known restriction properties. The probability measure can be thought of as a section of the determinant bundle over moduli spaces of Riemann surfaces. Loewner evolutions have a natural description in terms of random walk in the moduli space, and the stochastic diffusion equation translates to the Virasoro action of a certain weight-two operator on a uniformised version of the determinant bundle.

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