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The four-loop six-gluon NMHV ratio function

Dixon, Lance J. and von Hippel, Matt and McLeod, Andrew J. (2016) The four-loop six-gluon NMHV ratio function. Journal of High Energy Physics, 2016 (1). Art. No. 053. ISSN 1126-6708.

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We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N=4 super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of a Q differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi-Regge predictions at NNLL and N^3LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. We also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

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Additional Information:© 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: October 7, 2015; Accepted: November 23, 2015; Published: January 11, 2016. We are grateful to Benjamin Basso, Andrei Belitsky, Simon Caron-Huot, James Drummond, Song He, Yorgos Papathanasiou, Jeff Pennington, Amit Sever, Jara Trnka, and enlightening us about the Q equation, Simon also for comments on the manuscript, and Jeff for explaining his Lyndon reduction algorithm. This research was supported by the US Department of Energy under contract DE-AC02-76SF00515 and grant DE-SC0011632, by the Walter Burke Institute, by the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics, by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe", and by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. LD thanks Caltech, the Aspen Center for Physics and the NSF Grant #1066293 for hospitality, as well as the Galileo Galilei Institute and the Perimeter Institute for Theoretical Physics. MvH would like to thank the ICTP South American Institute for Fundamental Research for hospitality while this work was completed.
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-76SF00515
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Gordon and Betty Moore Foundation776
Munich Institute for Astro- and Particle Physics (MIAPP)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Government of Canada Industry Canada UNSPECIFIED
Province of Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Subject Keywords:Scattering Amplitudes; Supersymmetric gauge theory; 1/N Expansion
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Record Number:CaltechAUTHORS:20151022-122311732
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:61425
Deposited By: Joy Painter
Deposited On:22 Oct 2015 20:17
Last Modified:11 Mar 2016 21:57

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