The Three-loop MHV Octagon from $\bar{Q}$ equations

Abstract

The $\bar{Q}$ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. By using the $\bar{Q}$ equations, we compute the symbol of the first MHV amplitude with algebraic letters -- the three-loop 8-point amplitude (or the octagon remainder function) -- in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

20 pages, 1 figure

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• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
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Cited by in corpus (12)

• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Schubert Problems, Positivity and Symbol Letters
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• An Infinite Family of Elliptic Ladder Integrals
• Relativistic composite-particle theory of the gravitational form factors of pion: quantitative results
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The two-loop eight-point amplitude in ABJM theory
• An Origin Story for Amplitudes
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills