Abstract
Stochastic Loewner evolutions (SLE κ ) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLE κ evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLE κ processes and on the identification of the proper hull boundary states. This allows us to define an infinite set of SLE κ 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 SLE κ evolutions. We point out a relation between SLE κ processes and two dimensional gravity and conjecture a reconstruction procedure of conformal field theories from SLE κ data.
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Communicated by A. Kupiainen
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Bauer, M., Bernard, D. Conformal Field Theories of Stochastic Loewner Evolutions. Commun. Math. Phys. 239, 493–521 (2003). https://doi.org/10.1007/s00220-003-0881-x
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DOI: https://doi.org/10.1007/s00220-003-0881-x