Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-02
Commun.Math.Phys.239:493-521,2003
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, 3 figures, to appear in Commun. Math. Phys
Scientific paper
10.1007/s00220-003-0881-x
Stochastic Loewner evolutions (SLE) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLE evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLE processes and on the identification of the proper hull boundary states. This allows us to define an infinite set of SLE 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 evolutions. We point out a relation between SLE processes and two dimensional gravity and conjecture a reconstruction procedure of conformal field theories from SLE data.
Bauer Michel
Bernard Denis
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