Conformal Field Theories of Stochastic Loewner Evolutions

By Michel Bauer, D. Bernard. 2002

205 citations recorded by the source corpus.

Stochastic Loewner evolutions (SLEκ) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLEκ evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLEκ processes and on the identification of the proper hull boundary states. This allows us to define an infinite set of SLEκ zero modes, or martingales, whose existence is a consequence of the existence of a null vector in the appropriate Virasoro modules. This identification leads, for instance, to linear systems for generalized crossing probabilities whose coefficients are multipoint CFT correlation functions. It provides a direct link between conformal correlation functions and probabilities of stopping time events in SLEκ evolutions. We point out a relation between SLEκ processes and two dimensional gravity and conjecture a reconstruction procedure of conformal field theories from SLEκ data.

Subfields: Condensed Matter Physics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7efc3fae5b03962511850386329bad2d9a215a3e

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Citations in the corpus

Conformal restriction: The chordal case (2002, background): “See also [2, 3] for aspects of SLE from a CFT perspective.”
Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales (2005, methodology): “The connection between CFT and SLE is now well understood [8, 7, 9, 11, 12, 14] and the interplay between the two approaches has proved fruitful.”