Amplitudes and correlators to ten loops using simple, graphical bootstraps

Jacob L. Bourjaily, Paul Heslop, Vuong Viet Tran

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at:

Original languageEnglish (US)
Article number125
JournalJournal of High Energy Physics
Issue number11
StatePublished - Nov 1 2016

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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