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.
{ "_oai": { "updated": "2023-02-24T00:32:50Z", "id": "oai:repo.scoap3.org:73655", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "United Arab Emirates", "value": "Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates", "organization": "New York University Abu Dhabi" }, { "country": "USA", "value": "Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA", "organization": "New York University" }, { "country": "Netherlands", "value": "Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1111, Amsterdam, 1081 HV, The Netherlands", "organization": "Vrije Universiteit Amsterdam" } ], "surname": "Camia", "email": "federico.camia@nyu.edu", "full_name": "Camia, Federico", "given_names": "Federico" }, { "affiliations": [ { "country": "United Arab Emirates", "value": "Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates", "organization": "New York University Abu Dhabi" } ], "surname": "Foit", "email": "foit@nyu.edu", "full_name": "Foit, Valentino", "given_names": "Valentino" }, { "affiliations": [ { "country": "United Arab Emirates", "value": "Science Division, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, United Arab Emirates", "organization": "New York University Abu Dhabi" } ], "surname": "Gandolfi", "email": "albertogandolfi@nyu.edu", "full_name": "Gandolfi, Alberto", "given_names": "Alberto" }, { "affiliations": [ { "country": "USA", "value": "Center for Cosmology and Particle Physics, New York University, 726 Broadway, New York, NY, 10003, USA", "organization": "New York University" } ], "surname": "Kleban", "email": "kleban@nyu.edu", "full_name": "Kleban, Matthew", "given_names": "Matthew" } ], "titles": [ { "source": "Springer", "title": "The Brownian loop soup stress-energy tensor" } ], "dois": [ { "value": "10.1007/JHEP11(2022)009" } ], "publication_info": [ { "page_end": "26", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2022", "artid": "JHEP11(2022)009", "year": 2022, "page_start": "1", "journal_issue": "11" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-02-24T00:31:11.467637", "source": "Springer", "method": "Springer", "submission_number": "5f487fa6b3da11eda920065bd8dc6b20" }, "page_nr": [ 26 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2022" } ], "control_number": "73655", "record_creation_date": "2022-11-03T09:30:21.517355", "_files": [ { "checksum": "md5:63a4889447af9221baf7d549925b1e66", "filetype": "xml", "bucket": "2f20b0f3-5dbd-4457-9c46-06248008a573", "version_id": "48c92a33-3c08-4220-8867-02eb2099823a", "key": "10.1007/JHEP11(2022)009.xml", "size": 13600 }, { "checksum": "md5:c6af872a7eeecef4a83471796366ea54", "filetype": "pdf/a", "bucket": "2f20b0f3-5dbd-4457-9c46-06248008a573", "version_id": "f3f5e627-43b4-436d-8345-0f9bd91c5381", "key": "10.1007/JHEP11(2022)009_a.pdf", "size": 1052974 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "math-ph", "cond-mat.stat-mech", "hep-th", "math.MP", "math.PR" ], "value": "2112.00074" } ], "abstracts": [ { "source": "Springer", "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." } ], "imprints": [ { "date": "2022-11-02", "publisher": "Springer" } ] }