Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

Ambrosio, Raquel G.; Eden, Burkhard; Goddard, Timothy; Heslop, Paul; Taylor, Charles

Abstract

Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory methods the integrand of the four-point function of energy-momentum multiplets has been constructed up to six loops in previous work. In this article we extend this analysis to seven loops and use it to construct the full integrand of the five-point amplitude up to five loops, and in the parity even sector to six loops. All results, both parity even and parity odd, are obtained in a concise local form in dual momentum space and can be displayed efficiently through graphs. We have verified agreement with other local formulae both in terms of supertwistors and scalar momentum integrals as well as BCJ forms where those exist in the literature, i.e. up to three loops. Finally we note that the four-point correlation function can be extracted directly from the four-point amplitude and so this uncovers a direct link from four- to five-point amplitudes.

Citation

Ambrosio, R. G., Eden, B., Goddard, T., Heslop, P., & Taylor, C. (2015). Local integrands for the five-point amplitude in planar N=4 SYM up to five loops. Journal of High Energy Physics, 2015(1), Article 116. https://doi.org/10.1007/jhep01%282015%29116

• Journal Article Type: Article
• Acceptance Date: Dec 15, 2014
• Online Publication Date: Jan 13, 2015
• Publication Date: Jan 21, 2015
• Deposit Date: May 2, 2014
• Publicly Available Date: Jan 7, 2015
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 1
• Article Number: 116
• DOI: https://doi.org/10.1007/jhep01%282015%29116
• Public URL: https://durham-repository.worktribe.com/output/1455850
• Related Public URLs: http://arxiv.org/pdf/1312.1163.pdf