Abstract
Abstract
The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ > 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 = 2λ. 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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference25 articles.
1. G.F. Lawler and W. Werner, The Brownian loop soup, Probab. Theor. Related Fields 128 (2004) 565.
2. K. Symanzik, Euclidean quantum field theory, in 45th International School of Physics ‘Enrico Fermi’: Local Quantum Theory, Varenna Italy, August 12–24 1968 [Conf. Proc. C 680812 (1968) 152] [INSPIRE].
3. F. Camia, A. Gandolfi and M. Kleban, Conformal Correlation Functions in the Brownian Loop Soup, Nucl. Phys. B 902 (2016) 483 [arXiv:1501.05945] [INSPIRE].
4. F. Camia, V.F. Foit, A. Gandolfi and M. Kleban, Exact Correlation Functions in the Brownian Loop Soup, JHEP 07 (2020) 067 [arXiv:1912.00973] [INSPIRE].
5. F. Camia, V.F. Foit, A. Gandolfi and M. Kleban, Scalar conformal primary fields in the Brownian loop soup, arXiv:2109.12116.