Triangulation of 2-loop MHV Amplituhedron from Sign Flips

Abstract

In this paper, we consider the triangulation of 2-loop MHV amplituhedron from "sign flip" definition. Using the isomorphism between $m=2,k=2$ tree amplituhedron and 1-loop MHV physical amplituhedron, we found the direct triangulation of 2-loop MHV amplituhedron from sign flip. This triangulation is different from the BCFW triangulation because of the structure of the cells. And we also found a formula of the canonical form of $n$-point 2-loop MHV amplituhedron. This formula looks like a 2-loop version of the Kermit representation of 1-loop MHV amplitude. We checked that the sum of these cells of direct triangulation and BCFW or double pentagon diagram, these are consistent up to at least 22-pt amplitude numerically.

arXiv comment33 pages, 4 figures,

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Cited by in corpus (6)

• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Amplituhedra, and Beyond
• Sign Flip Triangulations of the Amplituhedron
• Internal boundaries of the loop amplituhedron
• Triangulation-free Trivialization of 2-loop MHV Amplituhedron
• Leading singularities and chambers of Correlahedron