  We study structural properties of the q-color Potts field theory which, for
real values of q, describes the scaling limit of the random cluster model. We
show that the number of independent n-point Potts spin correlators coincides
with that of independent n-point cluster connectivities and is given by
generalized Bell numbers. Only a subset of these spin correlators enters the
determination of the Potts magnetic properties for q integer. The structure of
the operator product expansion of the spin fields for generic q is also
identified. For the two-dimensional case, we analyze the duality relation
between spin and kink field correlators, both for the bulk and boundary cases,
obtaining in particular a sum rule for the kink-kink elastic scattering
amplitudes.
