Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps

Abstract

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: http://goo.gl/JH0yEc.

35 pages, 52 figures, and 6 tables. Complete expressions for the amplitude and correlator through ten loops can be obtained at: http://goo.gl/JH0yEc

References in corpus (10)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
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• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Notes on the scattering amplitude / Wilson loop duality