Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell scattering amplitudes. Working in a dimensionally-regularised ϕ 3 model at the conformal fixed point, we show that the on-shell renormalised amplitudes satisfy anomalous conformal Ward identities. Each external on-shell state contributes two terms to the anomaly. The first term is proportional to the elementary field anomalous dimension, and thus involves only lower-loop information. We show that the second term can be given as the convolution of a universal collinear function and lower-order amplitudes. The computation of the conformal anomaly is therefore simpler than that of the amplitude at the same perturbative order, which gives our anomalous conformal Ward identities a strong predictive power in perturbation theory. Finally, we show that our result is also of practical importance for dimensionally-regularised amplitudes away from the conformal fixed point.
{ "_oai": { "updated": "2023-09-24T00:34:43Z", "id": "oai:repo.scoap3.org:78437", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "France", "value": "LAPTh, Universit\u00e9 Savoie Mont Blanc, CNRS, Annecy-le-Vieux, F-74941, France", "organization": "LAPTh, Universit\u00e9 Savoie Mont Blanc, CNRS" } ], "surname": "Chicherin", "email": "chicherin@lapth.cnrs.fr", "full_name": "Chicherin, Dmitry", "given_names": "Dmitry" }, { "affiliations": [ { "country": "Germany", "value": "Max-Planck-Institut f\u00fcr Physik, Werner-Heisenberg-Institut, M\u00fcnchen, D-80805, Germany", "organization": "Werner-Heisenberg-Institut" } ], "surname": "Henn", "email": "henn@mpp.mpg.de", "full_name": "Henn, Johannes", "given_names": "Johannes" }, { "affiliations": [ { "country": "Italy", "value": "Dipartimento di Fisica and Arnold-Regge Center, Universit\u00e0 di Torino, and INFN, Sezione di Torino, Via P. Giuria 1, Torino, I-10125, Italy", "organization": "Dipartimento di Fisica and Arnold-Regge Center, Universit\u00e0 di Torino, and INFN, Sezione di Torino" } ], "surname": "Zoia", "email": "simone.zoia@unito.it", "full_name": "Zoia, Simone", "given_names": "Simone" } ], "titles": [ { "source": "Springer", "title": "Anomalous Ward identities for on-shell amplitudes at the conformal fixed point" } ], "dois": [ { "value": "10.1007/JHEP06(2023)110" } ], "publication_info": [ { "page_end": "57", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2023", "artid": "JHEP06(2023)110", "year": 2023, "page_start": "1", "journal_issue": "6" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-09-24T00:32:20.397454", "source": "Springer", "method": "Springer", "submission_number": "7ecceed25a7111ee9688729695cabdc8" }, "page_nr": [ 57 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2023" } ], "control_number": "78437", "record_creation_date": "2023-06-21T06:30:06.105655", "_files": [ { "checksum": "md5:f7ede74025c2e2e1899f106a0a458d16", "filetype": "xml", "bucket": "109ae784-ed24-4d5c-afec-434f108b289a", "version_id": "3be035b8-9cf4-4381-8de6-07adc93845a6", "key": "10.1007/JHEP06(2023)110.xml", "size": 12319 }, { "checksum": "md5:6848388ab4bac1bb83c51570c8e16b47", "filetype": "pdf/a", "bucket": "109ae784-ed24-4d5c-afec-434f108b289a", "version_id": "e60275ff-03b5-47e0-ae67-0522baa1d475", "key": "10.1007/JHEP06(2023)110_a.pdf", "size": 1158226 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "hep-ph" ], "value": "2207.12249" } ], "abstracts": [ { "source": "Springer", "value": "Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell scattering amplitudes. Working in a dimensionally-regularised \u03d5 3 model at the conformal fixed point, we show that the on-shell renormalised amplitudes satisfy anomalous conformal Ward identities. Each external on-shell state contributes two terms to the anomaly. The first term is proportional to the elementary field anomalous dimension, and thus involves only lower-loop information. We show that the second term can be given as the convolution of a universal collinear function and lower-order amplitudes. The computation of the conformal anomaly is therefore simpler than that of the amplitude at the same perturbative order, which gives our anomalous conformal Ward identities a strong predictive power in perturbation theory. Finally, we show that our result is also of practical importance for dimensionally-regularised amplitudes away from the conformal fixed point." } ], "imprints": [ { "date": "2023-06-19", "publisher": "Springer" } ] }