The University of Southampton
University of Southampton Institutional Repository
 ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

# Heptagons from the Steinmann Cluster Bootstrap

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].

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.

Text
publication version - Version of Record
Other
pdf

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

## Catalogue record

Date deposited: 01 Jun 2017 04:06

## Contributors

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