4-particle Amplituhedron at 3-loop and its Mondrian Diagrammatic Implication

Abstract

This article provides a direct calculation of the 4-particle amplituhedron at 3-loop order, by introducing a set of practical tricks. After delicately rearranging each piece of this calculation, we find a suggestive connection between positivity conditions and Mondrian diagrams, which will be quantitatively defined. Such a pattern can be generalized for all Mondrian diagrams among all those contribute to the 4-particle integrand of planar N=4 SYM to all loop orders, as a subsequent work 1712.09994 will show.

32 pages, 3 figures, 1 appendix. Figures improved for v3

References in corpus (2)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

Cited by in corpus (6)

• Sign Flip Triangulations of the Amplituhedron
• All-loop cuts from the Amplituhedron
• Internal boundaries of the loop amplituhedron
• Triangulation of 2-loop MHV Amplituhedron from Sign Flips
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron
• The twistor Wilson loop and the amplituhedron