Two-loop scattering amplitudes from the Riemann sphere

Author: 

Geyer, Y
Mason, L
Monteiro, R
Tourkine, P

Publication Date: 

30 December 2016

Journal: 

PHYSICAL REVIEW D

Last Updated: 

2019-12-12T09:00:30.34+00:00

Issue: 

12

Volume: 

94

DOI: 

10.1103/PhysRevD.94.125029

abstract: 

© 2016 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the «https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. The scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the world sheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the color dependence, which includes nonplanar contributions.

Symplectic id: 

667797

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article