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Folding Amplitudes into Form Factors: An Antipodal Duality

Folding Amplitudes into Form Factors: An Antipodal Duality
Folding Amplitudes into Form Factors: An Antipodal Duality
We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving surface. Up to a simple variable substitution, the map between these two quantities is given by the antipode operation defined on polylogarithms (as part of their Hopf algebra structure), which acts at symbol level by reversing the order of letters in each term. We provide evidence for this duality through seven loops.
hep-ph, hep-th
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Gurdogan, Omer
841de8b6-4eb2-407f-a4c4-c8136403794d
McLeod, Andrew J.
9e943513-29be-4efe-9a93-87f96afd071a
Wilhelm, Matthias
79808605-9a18-46ed-bad3-848349235708
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Gurdogan, Omer
841de8b6-4eb2-407f-a4c4-c8136403794d
McLeod, Andrew J.
9e943513-29be-4efe-9a93-87f96afd071a
Wilhelm, Matthias
79808605-9a18-46ed-bad3-848349235708

Dixon, Lance J., Gurdogan, Omer, McLeod, Andrew J. and Wilhelm, Matthias (2022) Folding Amplitudes into Form Factors: An Antipodal Duality. Phys.Rev.Lett., 128 (11), [111602]. (doi:10.1103/PhysRevLett.128.111602).

Record type: Article

Abstract

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving surface. Up to a simple variable substitution, the map between these two quantities is given by the antipode operation defined on polylogarithms (as part of their Hopf algebra structure), which acts at symbol level by reversing the order of letters in each term. We provide evidence for this duality through seven loops.

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More information

Accepted/In Press date: 12 December 2021
e-pub ahead of print date: 15 March 2022
Additional Information: 5+2 pages, 2 figures, 2 tables. v2: added further checks at kinematic points, some clarifications and references; version to appear in PRL
Keywords: hep-ph, hep-th

Identifiers

Local EPrints ID: 472310
URI: http://eprints.soton.ac.uk/id/eprint/472310
PURE UUID: 53831e0b-4fa7-42a3-9ccc-1217d41554dc

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Date deposited: 30 Nov 2022 18:12
Last modified: 30 Nov 2022 18:13

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Contributors

Author: Lance J. Dixon
Author: Omer Gurdogan
Author: Andrew J. McLeod
Author: Matthias Wilhelm

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