The correlator toolbox, metrics and moduli Original Research Article

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 image. 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 image in terms of conformally invariant random growing compact subsets of polygons. Further, we also mention a related class of polyhedral image processes. In the case of polygons, the parameters image are related to the exterior angles. We also show that image 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.