CFT Interpretation of Merging Multiple SLE Traces

Abstract

In this paper we give a physical interpretation of the probability of a Stochastic Loewner Evolution (SLE) trace approaching a marked point in the upper half plane, e.g. on another trace. Our approach is based on the concept of fusion of boundary with bulk or other boundary fields in Conformal Field Theory (CFT). In this context we also state a proposal how the results can be extended to situations that happen not sufficiently far away from the boundary.