On Malliavin Measures, SLE, and CFT

This paper is dedicated to the 70th birthday of V. Arnol'd. The paper is motivated by emerging connections between the conformal field theory (CFT) on the one hand and stochastic Löwner evolution (SLE) processes and measures that play the role of the Haar measures for the diffeomorphism group of a circle, on the other hand. We attempt to build a framework for widely spread beliefs that SLE processes would provide a picture of phase separation in a small massive perturbation of the CFT.