  SLE_k 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_k 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_k=(3k-8)(6/k-1)/2 and
zero modes -- observables which are conserved in mean -- of the SLE_k
stochastic processes.
