The Brownian loop soup stress-energy tensor

Abstract

The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity $\lambda >0$. Recently, we constructed families of operators in the BLS and showed that they transform as conformal primary operators. In this paper we provide an explicit expression for the BLS stress-energy tensor and compute its operator product expansion with other operators. Our results are consistent with the conformal Ward identities and our previous result that the central charge is $c=2\lambda$. In the case of domains with boundary we identify a boundary operator that has properties consistent with the boundary stress-energy tensor. We show that this operator generates local deformations of the boundary and that it is related to a boundary operator that induces a Brownian excursion starting or ending at its insertion point.

24 pages, 3 figures

References in corpus (6)

• Two-Dimensional Critical Percolation: The Full Scaling Limit
• Conformal Correlation Functions in the Brownian Loop Soup
• Twist operator correlation functions in O(n) loop models
• Correlation functions of twist operators applied to single self-avoiding loops
• Exact Correlation Functions in the Brownian Loop Soup
• Scalar conformal primary fields in the Brownian loop soup