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Logarithmic Singularities and Maximally Supersymmetric Amplitudes

Bern, Zvi and Herrmann, Enrico and Litsey, Sean and Stankowicz, James and Trnka, Jaroslav (2015) Logarithmic Singularities and Maximally Supersymmetric Amplitudes. Journal of High Energy Physics, 2015 (6). Art. No. 202. ISSN 1126-6708. doi:10.1007/JHEP06(2015)202.

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The dual formulation of planar =4 super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key integrand level analytic information contained in dual conformal symmetry. We also conjecture that to all loop orders, while N=8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. For the three-loop four-point N=4 super-Yang-Mills amplitude, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We then express the complete amplitude in terms of the basis diagrams, with the coefficients determined by unitarity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest via d log forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Furthermore, we present a variety of examples illustrating that these constraints are more restrictive than dual conformal symmetry. Our investigations show that the singularity structures of planar and nonplanar integrands in N=4 super-Yang-Mills are strikingly similar. While it is not clear how to extend either dual conformal symmetry or a dual formulation to the nonplanar sector, these results suggest that related concepts might exist and await discovery. Finally, we describe the singularity structure of N=8 supergravity at three loops and beyond.

Item Type:Article
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URLURL TypeDescription Paper
Bern, Zvi0000-0001-9075-9501
Herrmann, Enrico0000-0002-3983-2993
Additional Information:© 2015 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 SCOAP. Received: January 14, 2015; Accepted: April 26, 2015; Published: June 30, 2015. We thank Nima Arkani-Hamed, Jacob Bourjaily, Scott Davies, Lance Dixon and Josh Nohle for helpful discussions. We especially thank Johannes Henn for discussions and detailed comparisons to unpublished results for various nonplanar master integrals. This work was supported in part by the US Department of Energy under Award Numbers DE-SC0009937 and DE-SC0011632. J. T. is supported in part by the David and Ellen Lee Postdoctoral Scholarship. E. H. is supported in part by a Dominic Orr Graduate Fellowship.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009937
Department of Energy (DOE)DE-SC0011632
David and Ellen Lee Postdoctoral ScholarshipUNSPECIFIED
Dominic Orr Graduate FellowshipUNSPECIFIED
Subject Keywords:Scattering Amplitudes, Extended Supersymmetry
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Issue or Number:6
Record Number:CaltechAUTHORS:20150114-204329121
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53750
Deposited By: Joy Painter
Deposited On:15 Jan 2015 17:11
Last Modified:10 Nov 2021 20:06

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