Triangulation-free Trivialization of 2-loop MHV Amplituhedron

Understand

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.