CFT Interpretation of Merging Multiple SLE Traces

TL;DR

This paper provides a conformal field theory interpretation of the probability that multiple SLE traces approach each other or a boundary point, using fusion concepts to extend understanding of boundary and bulk interactions.

Contribution

It introduces a CFT-based framework for interpreting SLE trace interactions and proposes extensions for near-boundary scenarios.

Findings

CFT interpretation of SLE trace approaching points

Fusion of boundary and bulk fields explains probabilities

Extension proposal for near-boundary interactions

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.