A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon
By J. Drummond, G. Papathanasiou, M. Spradlin. 2014
169 citations recorded by the source corpus.
A bstractSeven-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$$ \mathcal{A} $$-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 ∥ 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 threeloop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n > 6.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/879f396baadd56595c3686120ea9571f6e9feb1e
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In Nuclear and High Energy Physics
- M. Spradlin
- G. Papathanasiou
- L. Dixon
- M. Hippel
- J. Drummond
- Andrew J. McLeod
- T. Harrington
- S. Caron-Huot
Citations in the corpus
- Heptagons from the Steinmann cluster bootstrap (2016, methodology): “At seven points, the remainder function has been computed at two loops [57, 79–81] and its symbol has been computed at three loops [12].”
- The four-loop six-gluon NMHV ratio function (2015, background): “A similar heptagon function bootstrap, based on cluster variables [46, 47] has yielded the (symbol of the) seven-point remainder function — with remarkably little input from physical limits [48].”