### Abstract

We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

Original language | English (US) |
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Pages (from-to) | 483-507 |

Number of pages | 25 |

Journal | Nuclear Physics, Section B |

Volume | 902 |

DOIs | |

State | Published - Jan 1 2016 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*902*, 483-507. https://doi.org/10.1016/j.nuclphysb.2015.11.022

**Conformal correlation functions in the Brownian loop soup.** / Camia, Federico; Gandolfi, Alberto; Kleban, Matthew.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 902, pp. 483-507. https://doi.org/10.1016/j.nuclphysb.2015.11.022

}

TY - JOUR

T1 - Conformal correlation functions in the Brownian loop soup

AU - Camia, Federico

AU - Gandolfi, Alberto

AU - Kleban, Matthew

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

AB - We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.

UR - http://www.scopus.com/inward/record.url?scp=84949256384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949256384&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2015.11.022

DO - 10.1016/j.nuclphysb.2015.11.022

M3 - Article

AN - SCOPUS:84949256384

VL - 902

SP - 483

EP - 507

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -