Connecting SLE and minisuperspace Liouville gravity

Details Connecting SLE and minisuperspace Liouville gravity Connecting SLE and minisuperspace Liouville gravity

2007-09-24

arxiv.org/abs/0709.3664v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX

Scientific paper

We show that Fokker-Planck equation for chordal SLE process under a simple rescaling of the probability density can be traced to the minisuperspace Wheeler-de Witt equation for boundary operator in 2d Liouville gravity. Insertion of an operator, calculating SLE critical exponent, corresponds to adding matter contribution to WdW equation. This observation may be useful for understanding of why SLE critical exponents are given by KPZ gravitational scaling dimensions. Possible applications of the obtained relation are discussed.

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