We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin 1 and 2. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-K integrals and a differential operator which relates triple-K integrals with different indices. For several correlators, closed forms without the differential operator are also found.
{ "_oai": { "updated": "2019-05-10T21:31:07Z", "id": "oai:repo.scoap3.org:47233", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Thailand", "value": "Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand", "organization": "Chulalongkorn University" } ], "surname": "Isono", "email": "hiroshi.isono81@gmail.com", "full_name": "Isono, Hiroshi", "given_names": "Hiroshi" }, { "affiliations": [ { "country": "Japan", "value": "Department of Physics, Kobe University, Kobe, 657-8501, Japan", "organization": "Kobe University" } ], "surname": "Noumi", "email": "tnoumi@phys.sci.kobe-u.ac.jp", "full_name": "Noumi, Toshifumi", "given_names": "Toshifumi" }, { "affiliations": [ { "country": "Japan", "value": "Department of Physics, Kobe University, Kobe, 657-8501, Japan", "organization": "Kobe University" } ], "surname": "Takeuchi", "email": "toshi.takeuchi@stu.kobe-u.ac.jp", "full_name": "Takeuchi, Toshiaki", "given_names": "Toshiaki" } ], "titles": [ { "source": "Springer", "title": "Momentum space conformal three-point functions of conserved currents and a general spinning operator" } ], "dois": [ { "value": "10.1007/JHEP05(2019)057" } ], "publication_info": [ { "page_end": "41", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2019", "artid": "JHEP052019057", "year": 2019, "page_start": "1", "journal_issue": "5" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2019-05-10T23:30:52.650008", "source": "Springer", "method": "Springer", "submission_number": "c6deb09a736a11e99fff02163e01809a" }, "page_nr": [ 41 ], "license": [ { "url": "https://creativecommons.org/licenses/by/3.0", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2019" } ], "control_number": "47233", "record_creation_date": "2019-05-10T23:30:52.650036", "_files": [ { "checksum": "md5:83944ad2e51b426c481bb5276ea7dd95", "filetype": "xml", "bucket": "0a197676-8d65-4fa2-ae4c-bef179cd4cb0", "version_id": "92c23ab8-25dc-455e-82d6-929989fa5f73", "key": "10.1007/JHEP05(2019)057.xml", "size": 10492 }, { "checksum": "md5:3c51b1ed3bf57fccfca9e50ae1948534", "filetype": "pdf/a", "bucket": "0a197676-8d65-4fa2-ae4c-bef179cd4cb0", "version_id": "72d064f9-104f-4b73-b5bf-94afb338db19", "key": "10.1007/JHEP05(2019)057_a.pdf", "size": 727685 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "cond-mat.stat-mech", "math-ph", "math.MP" ], "value": "1903.01110" } ], "abstracts": [ { "source": "Springer", "value": "We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin 1 and 2. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-K integrals and a differential operator which relates triple-K integrals with different indices. For several correlators, closed forms without the differential operator are also found." } ], "imprints": [ { "date": "2019-05-10", "publisher": "Springer" } ] }