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Heptagons from the Steinmann Cluster Bootstrap

Heptagons from the Steinmann Cluster Bootstrap
Heptagons from the Steinmann Cluster Bootstrap
We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar $\mathcal{N} = 4$ supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal ($\bar{Q}$) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.
hep-th
1029-8479
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Harrington, Thomas
a39a6b7e-fd4f-4c44-b53b-16c8fbdaa7fa
McLeod, Andrew J.
9e943513-29be-4efe-9a93-87f96afd071a
Papathanasiou, Georgios
92cb6f58-cc1c-4166-8595-70b13c9ea734
Spradlin, Marcus
cb38721d-5588-4167-8200-ff8881004101
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Harrington, Thomas
a39a6b7e-fd4f-4c44-b53b-16c8fbdaa7fa
McLeod, Andrew J.
9e943513-29be-4efe-9a93-87f96afd071a
Papathanasiou, Georgios
92cb6f58-cc1c-4166-8595-70b13c9ea734
Spradlin, Marcus
cb38721d-5588-4167-8200-ff8881004101

Dixon, Lance J., Drummond, James, Harrington, Thomas, McLeod, Andrew J., Papathanasiou, Georgios and Spradlin, Marcus (2017) Heptagons from the Steinmann Cluster Bootstrap. Journal of High Energy Physics, 2017 (2), [137]. (doi:10.1007/JHEP02(2017)137).

Record type: Article

Abstract

We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar $\mathcal{N} = 4$ supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal ($\bar{Q}$) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

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Accepted/In Press date: 28 December 2016
e-pub ahead of print date: 28 February 2017
Published date: February 2017
Additional Information: 43 pages, 2 figures. v2: typos corrected; version to appear in JHEP
Keywords: hep-th
Organisations: Theory Group

Identifiers

Local EPrints ID: 409699
URI: http://eprints.soton.ac.uk/id/eprint/409699
ISSN: 1029-8479
PURE UUID: 89f7ecae-862a-4368-a14f-d7b4654aaba4

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Date deposited: 01 Jun 2017 04:06
Last modified: 25 Nov 2021 17:18

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Contributors

Author: Lance J. Dixon
Author: James Drummond
Author: Thomas Harrington
Author: Andrew J. McLeod
Author: Georgios Papathanasiou
Author: Marcus Spradlin

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