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arXiv · hep-th/0308020

On Conformal Field Theory and Stochastic Loewner Evolution

Roland Friedrich·Jussi Kalkkinen
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Abstract

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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Roland Friedrich, Jussi Kalkkinen. 2004-03-24. On Conformal Field Theory and Stochastic Loewner Evolution. https://doi.org/10.1016/j.nuclphysb.2004.03.025

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