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 Loewner 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 growing compact subsets of polygons. The parameters ρj are related to the exterior angles of the polygons. 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. PACS 2003: 02.50.Ey, 05.50.+q, 11.25.Hf MSC 2000: 60D05, 58J65, 81T40