Boundary operators in the Brownian loop soup

TL;DR

This paper identifies infinitely many boundary operators in the Brownian loop soup, linking conformal field theory with probabilistic properties of Brownian loops and their boundary interactions.

Contribution

It introduces a new class of boundary operators in the Brownian loop soup with integer conformal dimensions, derived from conformal block analysis.

Findings

Boundary operators have non-negative integer conformal dimensions.

Boundary operators correspond to inserting multiple outer boundaries of Brownian loops.

Provides a physical interpretation of boundary operators in terms of Brownian loop configurations.

Abstract

We obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of having two marked points on the upper half-plane being separated by Brownian loops. The resulting boundary operators are primary operators in a 2D CFT with central charge $c\leq1$ and have conformal dimensions that are non-negative integers. By comparing the above-mentioned conformal block expansion with probabilities in the Brownian loop soup, we provide a physical interpretation of the boundary operators of even dimensions as operators that insert multiple outer boundaries of Brownian loops at points on the real axis.