Triangulation-free trivialization of 2-loop MHV amplituhedron

Abstract

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 [6] for the multi-loop 4-particle amplituhedron. Moreover, the proof of 2-loop n-particle MHV amplituhedron in [4] 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.

Keywords

• Scattering Amplitudes
• Supersymmetric Gauge Theory