Triangulation-free Trivialization of 2-loop MHV Amplituhedron

Kojima, Ryota; Rao, Junjie

doi:10.1007/JHEP10(2020)140

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Triangulation-free Trivialization of 2-loop MHV Amplituhedron

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Rao, Junjie
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Kojima, R., & Rao, J. (2020). Triangulation-free Trivialization of 2-loop MHV Amplituhedron. Journal of High Energy Physics, 2020(10): 140. doi:10.1007/JHEP10(2020)140.

Cite as: https://hdl.handle.net/21.11116/0000-0007-00C6-9

Abstract

This article introduces a new approach to implement positivity for the 2-loop
n-particle MHV amplituhedron, circumventing the conventional triangulation with
respect to positive variables of each cell carved out by the sign flips. This
approach is universal for all linear positive conditions and hence free of
case-by-case triangulation, as an application of the trick of positive infinity
first introduced in 1910.14612 for the multi-loop 4-particle amplituhedron.
Moreover, the proof of 2-loop n-particle MHV amplituhedron in 1812.01822 is
revised, and we explain the nontriviality and difficulty of using conventional
triangulation while the results have a simple universal pattern. A further
example is presented to tentatively explore its generalization towards handling
multiple positive conditions at 3-loop and higher.