On Conformal Field Theory and Stochastic Loewner Evolution
نویسندگان
چکیده
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. PACS 2003: 02.50.Ey, 05.50.+q, 11.25.Hf MSC 2000: 60D05, 58J52, 58J65, 81T40
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