Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2015)072
Keywords
Supersymmetric gauge theory; Extended Supersymmetry; Scattering Amplitudes; 1/N Expansion
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Funding
- French National Agency for Research (ANR) [BLANC-SIMI-4-2011]
- U.S. Department of Energy [DE-SC0010010]
- CERN theory group
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Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the 7 parallel to 6 collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6.
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