The Brownian loop soup stress-energy tensor

Journal of High Energy Physics

Regular Article - Theoretical Physics

Matthew Kleban¹  Alberto Gandolfi²  Valentino F. Foit²  Federico Camia³ 

[1] Center for Cosmology and Particle Physics, New York University, 726 Broadway, 10003, New York, NY, USA;Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates;Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates;Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA;Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111, 1081 HV, Amsterdam, The Netherlands;

关键词: Scale and Conformal Symmetries;    Integrable Field Theories;    Random Systems;    Stochastic Processes;   

DOI  :  10.1007/JHEP11(2022)009

 received in 2022-02-25, accepted in 2022-10-23,  发布年份 2022

来源: Springer

【 摘 要 】

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.

【 授权许可】

Unknown   
© The Author(s) 2022