|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Positive geometry, local triangulations, and the dual of the Amplituhedron | | Enrico Herrmann
; Cameron Langer
; Jaroslav Trnka
; Minshan Zheng
; | | Date: |
11 Sep 2020 | | Abstract: | We initiate the systematic study of emph{local positive spaces} which arise
in the context of the Amplituhedron construction for scattering amplitudes in
planar maximally supersymmetric Yang-Mills theory. We show that all local
positive spaces relevant for one-loop MHV amplitudes are characterized by
certain sign-flip conditions and are associated with surprisingly simple
logarithmic forms. In the maximal sign-flip case they are finite one-loop
octagons. Particular combinations of sign-flip spaces can be glued into new
local positive geometries. These correspond to local pentagon integrands that
appear in the local expansion of the MHV one-loop amplitude. We show that,
geometrically, these pentagons do emph{not} triangulate the original
Amplituhedron space but rather its twin "Amplituhedron-Prime." This new
geometry has the same boundary structure as the Amplituhedron (and therefore
the same logarithmic form) but differs in the bulk as a geometric space. On
certain two-dimensional boundaries, where the Amplituhedron geometry reduces to
a polygon, we check that both spaces map to the same dual polygon.
Interestingly, we find that the pentagons internally triangulate that dual
space. This gives a direct evidence that the chiral pentagons are natural
building blocks for a yet-to-be discovered dual Amplituhedron. | | Source: | arXiv, 2009.05607 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER