SLEκ growth processes and conformal field theories

SLEkappa stochastic processes describe growth of random curves which, in some cases, may be identified with boundaries of two-dimensional critical percolating clusters. By generalizing SLEkappa growths to formal Markov processes on the central extension of the 2d conformal group, we establish a connection between conformal field theories with central charges c(kappa) = 1/2(3kappa - 8) (6/kappa - 1) and zero modes-observables which are conserved in mean-of the SLEkappa stochastic processes. (C) 2002 Elsevier Science B.V. All rights reserved.