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 sevenpoint amplitudes in planar $$ \mathcal{N} $$ = 4 supersymmetric YangMills theory, making higherloop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and welldefined collinear limits suffice to determine uniquely the symbols of the threeloop NMHV and fourloop MHV sevenpoint 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.
 Authors:

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 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Univ. of Southampton (United Kingdom). School of Physics and Astronomy
 Brown Univ., Providence, RI (United States). Dept. of Physics
 SLAC National Accelerator Lab., Menlo Park, CA (United States); Deutsches ElektronenSynchrotron (DESY), Hamburg (Germany). DESY Theory Group
 Publication Date:
 Report Number(s):
 SLACPUB16894
Journal ID: ISSN 10298479; arXiv:1612.08976; TRN: US1700677
 Grant/Contract Number:
 AC0276SF00515
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HEPTH; Scattering Amplitudes; Supersymmetric gauge theory
 OSTI Identifier:
 1339540
Dixon, Lance J., Drummond, James, Harrington, Thomas, McLeod, Andrew J., Papathanasiou, Georgios, and Spradlin, Marcus. Heptagons from the Steinmann cluster bootstrap. United States: N. p.,
Web. doi:10.1007/JHEP02(2017)137.
Dixon, Lance J., Drummond, James, Harrington, Thomas, McLeod, Andrew J., Papathanasiou, Georgios, & Spradlin, Marcus. Heptagons from the Steinmann cluster bootstrap. United States. doi:10.1007/JHEP02(2017)137.
Dixon, Lance J., Drummond, James, Harrington, Thomas, McLeod, Andrew J., Papathanasiou, Georgios, and Spradlin, Marcus. 2017.
"Heptagons from the Steinmann cluster bootstrap". United States.
doi:10.1007/JHEP02(2017)137. https://www.osti.gov/servlets/purl/1339540.
@article{osti_1339540,
title = {Heptagons from the Steinmann cluster bootstrap},
author = {Dixon, Lance J. and Drummond, James and Harrington, Thomas and McLeod, Andrew J. and Papathanasiou, Georgios and Spradlin, Marcus},
abstractNote = {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 sevenpoint amplitudes in planar $ \mathcal{N} $ = 4 supersymmetric YangMills theory, making higherloop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and welldefined collinear limits suffice to determine uniquely the symbols of the threeloop NMHV and fourloop MHV sevenpoint 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.},
doi = {10.1007/JHEP02(2017)137},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2017,
place = {United States},
year = {2017},
month = {2}
}