Boundary operators in the Brownian loop soup

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.