  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.
