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arXiv · 1812.01822

Triangulation of 2-loop MHV Amplituhedron from Sign Flips

Ryota Kojima
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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.

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Ryota Kojima. 2018-12-05. Triangulation of 2-loop MHV Amplituhedron from Sign Flips. https://doi.org/10.1007/jhep04(2019)085

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