SLEκ growth processes and conformal field theories

SLEκ stochastic processes describe growth of random curves which, in some cases, may be identified with boundaries of two-dimensional critical percolating clusters. By generalizing SLEκ 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 cκ=12(3κ−8)(6κ−1) and zero modes—observables which are conserved in mean—of the SLEκ stochastic processes.