The Brownian loop soup stress-energy tensor

Federico Camia, Valentino F. Foit, Alberto Gandolfi, Matthew Kleban

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number9
JournalJournal of High Energy Physics
Issue number11
StatePublished - Nov 2022


  • Integrable Field Theories
  • Random Systems
  • Scale and Conformal Symmetries
  • Stochastic Processes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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