Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
Abstract 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 a...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-06-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2023)110 |
| _version_ | 1827808212371374080 |
|---|---|
| author | Dmitry Chicherin Johannes Henn Simone Zoia |
| author_facet | Dmitry Chicherin Johannes Henn Simone Zoia |
| author_sort | Dmitry Chicherin |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-03-11T22:20:51Z |
| format | Article |
| id | doaj.art-4ef12dc6088f4ad8a11e85af79e8e238 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T22:20:51Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4ef12dc6088f4ad8a11e85af79e8e2382023-09-24T11:05:21ZengSpringerOpenJournal of High Energy Physics1029-84792023-06-012023615710.1007/JHEP06(2023)110Anomalous Ward identities for on-shell amplitudes at the conformal fixed pointDmitry Chicherin0Johannes Henn1Simone Zoia2LAPTh, Université Savoie Mont Blanc, CNRSMax-Planck-Institut für Physik, Werner-Heisenberg-InstitutDipartimento di Fisica and Arnold-Regge Center, Università di Torino, and INFN, Sezione di TorinoAbstract 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.https://doi.org/10.1007/JHEP06(2023)110Scale and Conformal SymmetriesScattering Amplitudes |
| spellingShingle | Dmitry Chicherin Johannes Henn Simone Zoia Anomalous Ward identities for on-shell amplitudes at the conformal fixed point Journal of High Energy Physics Scale and Conformal Symmetries Scattering Amplitudes |
| title | Anomalous Ward identities for on-shell amplitudes at the conformal fixed point |
| title_full | Anomalous Ward identities for on-shell amplitudes at the conformal fixed point |
| title_fullStr | Anomalous Ward identities for on-shell amplitudes at the conformal fixed point |
| title_full_unstemmed | Anomalous Ward identities for on-shell amplitudes at the conformal fixed point |
| title_short | Anomalous Ward identities for on-shell amplitudes at the conformal fixed point |
| title_sort | anomalous ward identities for on shell amplitudes at the conformal fixed point |
| topic | Scale and Conformal Symmetries Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP06(2023)110 |
| work_keys_str_mv | AT dmitrychicherin anomalouswardidentitiesforonshellamplitudesattheconformalfixedpoint AT johanneshenn anomalouswardidentitiesforonshellamplitudesattheconformalfixedpoint AT simonezoia anomalouswardidentitiesforonshellamplitudesattheconformalfixedpoint |