SLEκ growth processes and conformal field theories

Abstract SLE κ stochastic processes describe growth of random curves which, in some cases, may be identified with boundaries of two-dimensional critical percolating clusters. By generalizing SLE κ 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 κ = 1 2 (3κ−8)( 6 κ −1) and zero modes—observables which are conserved in mean—of the SLE κ stochastic processes.