The Brownian loop soup stress-energy tensor

Federico Camia (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, New York, NY, 10012, USA; Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111, Amsterdam, 1081 HV, The Netherlands) ; Valentino Foit (Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates) ; Alberto Gandolfi (Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates) ; Matthew Kleban (Center for Cosmology and Particle Physics, New York University, 726 Broadway, New York, NY, 10003, USA)

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.

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      "value": "The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity \u03bb > 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\u03bb. 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."
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Published on:
02 November 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 11
Pages 1-26
DOI:
https://doi.org/10.1007/JHEP11(2022)009
arXiv:
2112.00074
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: