One-loop amplitudes on the Riemann sphere

A bstract 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...

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Bibliographic Details
Published in:The journal of high energy physics 2016-03, Vol.2016 (3), p.1-53, Article 114
Main Authors: Geyer, Yvonne, Mason, Lionel, Monteiro, Ricardo, Tourkine, Piotr
Format: Article
Language:English
Subjects:
Amplitudes
Classical and Quantum Gravitation
Correlation
Derivation
Elementary Particles
Formulas (mathematics)
Gravitation
High energy physics
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering
Scattering amplitude
String Theory
Supergravity
Toruses
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2016)114