One-loop amplitudes on the Riemann sphere
The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced...
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Published: |
Springer
2016
|
| _version_ | 1826292203913216000 |
|---|---|
| author | Geyer, Y Mason, L Monteiro, R Tourkine, P |
| author_facet | Geyer, Y Mason, L Monteiro, R Tourkine, P |
| author_sort | Geyer, Y |
| collection | OXFORD |
| description | The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced to the Riemann sphere and checked in simple cases. We also proposed analogous formulae for other theories including maximal super-Yang-Mills theory and supergravity in other dimensions at one loop. We give further details of these results and extend them in two directions. Firstly, we propose new formulae for the one-loop integrands of Yang-Mills theory and gravity in the absence of supersymmetry. These follow from the identification of the states running in the loop as expressed in the ambitwistor-string correlator. Secondly, we give a systematic proof of the non-supersymmetric formulae using the worldsheet factorisation properties of the nodal Riemann sphere underlying the scattering equations at one loop. Our formulae have the same decomposition under the recently introduced Q-cuts as one-loop integrands and hence give the correct amplitudes. |
| first_indexed | 2024-03-07T03:11:04Z |
| format | Journal article |
| id | oxford-uuid:b4381346-be94-4b89-a865-8d56250d600d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:11:04Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:b4381346-be94-4b89-a865-8d56250d600d2022-03-27T04:24:36ZOne-loop amplitudes on the Riemann sphereJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b4381346-be94-4b89-a865-8d56250d600dSymplectic Elements at OxfordSpringer2016Geyer, YMason, LMonteiro, RTourkine, PThe scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced to the Riemann sphere and checked in simple cases. We also proposed analogous formulae for other theories including maximal super-Yang-Mills theory and supergravity in other dimensions at one loop. We give further details of these results and extend them in two directions. Firstly, we propose new formulae for the one-loop integrands of Yang-Mills theory and gravity in the absence of supersymmetry. These follow from the identification of the states running in the loop as expressed in the ambitwistor-string correlator. Secondly, we give a systematic proof of the non-supersymmetric formulae using the worldsheet factorisation properties of the nodal Riemann sphere underlying the scattering equations at one loop. Our formulae have the same decomposition under the recently introduced Q-cuts as one-loop integrands and hence give the correct amplitudes. |
| spellingShingle | Geyer, Y Mason, L Monteiro, R Tourkine, P One-loop amplitudes on the Riemann sphere |
| title | One-loop amplitudes on the Riemann sphere |
| title_full | One-loop amplitudes on the Riemann sphere |
| title_fullStr | One-loop amplitudes on the Riemann sphere |
| title_full_unstemmed | One-loop amplitudes on the Riemann sphere |
| title_short | One-loop amplitudes on the Riemann sphere |
| title_sort | one loop amplitudes on the riemann sphere |
| work_keys_str_mv | AT geyery oneloopamplitudesontheriemannsphere AT masonl oneloopamplitudesontheriemannsphere AT monteiror oneloopamplitudesontheriemannsphere AT tourkinep oneloopamplitudesontheriemannsphere |