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Title: 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.
ORCiD logo [1] ;  [2] ;  [3] ;  [1] ;  [4] ;  [3]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Univ. of Southampton (United Kingdom). School of Physics and Astronomy
  3. Brown Univ., Providence, RI (United States). Dept. of Physics
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). DESY Theory Group
Publication Date:
Report Number(s):
Journal ID: ISSN 1029-8479; arXiv:1612.08976; TRN: US1700677
Grant/Contract Number:
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 1029-8479
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HEPTH; Scattering Amplitudes; Supersymmetric gauge theory
OSTI Identifier: