| Autor: |
Gabriele Dian, Paul Heslop, Alastair Stewart |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
SciPost Physics, Vol 15, Iss 3, p 098 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2542-4653 |
| DOI: |
10.21468/SciPostPhys.15.3.098 |
| Popis: |
The strict definition of positive geometry implies that all maximal residues of its canonical form are $± 1$. We observe, however, that the loop integrand of the amplitude in planar ${\cal N}=4$ super Yang-Mills has maximal residues not equal to $± 1$. We find the reason for this is that deep in the boundary structure of the loop amplituhedron there are geometries which contain internal boundaries: codimension one defects separating two regions of opposite orientation. This phenomenon requires a generalisation of the concept of positive geometry and canonical form to include such internal boundaries and also suggests the utility of a further generalisation to `weighted positive geometries'. We re-examine the deepest cut of ${\cal N}=4$ amplitudes in light of this and obtain new all order residues. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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