The correlator toolbox, metrics and moduli

We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Löwner type procedure to generalisations of SLE (κ, ρ). We also highlight the necessity of moduli for a consistent kinematic description of these more general stochastic processes. As an illustration we give a geometric derivation of SLE(κ, ρ) in terms of conformally invariant random growinginf compact subsets of polygons. Further, we also mention a related class of polyhedral SLE (κ, ρ, ρ) processes. In the case of polygons, the parameters ρ_j are related to the exterior angles. We also show that SLE (κ, ρ) can be generated by a Brownian motion in a gravitational background, where the metric and the Brownian motion are coupled. The metric is obtained as the pull-back of the Euclidean metric of a fluctuating polygon.