Volumes of polytopes without triangulations
Abstract The geometry of the dual amplituhedron is generally described in reference to a particular triangulation. A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this geometry without reference to a particular triangulatio...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2017)071 |
| _version_ | 1818421016054988800 |
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| author | Michael Enciso |
| author_facet | Michael Enciso |
| author_sort | Michael Enciso |
| collection | DOAJ |
| description | Abstract The geometry of the dual amplituhedron is generally described in reference to a particular triangulation. A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this geometry without reference to a particular triangulation is desirable. In this note we introduce a new for-malism for computing the volumes of general polytopes in any dimension. We define new “vertex objects” and introduce a calculus for expressing volumes of polytopes in terms of them. These expressions are unique, independent of any triangulation, manifestly depend only on the vertices of the underlying polytope, and can be used to easily derive identities amongst different triangulations. As one application of this formalism, we obtain new expressions for the volume of the tree-level, n-point NMHV dual amplituhedron. |
| first_indexed | 2024-12-14T13:03:39Z |
| format | Article |
| id | doaj.art-8701d62e759c455798aea2d73441d6d6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T13:03:39Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8701d62e759c455798aea2d73441d6d62022-12-21T23:00:22ZengSpringerOpenJournal of High Energy Physics1029-84792017-10-0120171013210.1007/JHEP10(2017)071Volumes of polytopes without triangulationsMichael Enciso0Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California at Los AngelesAbstract The geometry of the dual amplituhedron is generally described in reference to a particular triangulation. A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this geometry without reference to a particular triangulation is desirable. In this note we introduce a new for-malism for computing the volumes of general polytopes in any dimension. We define new “vertex objects” and introduce a calculus for expressing volumes of polytopes in terms of them. These expressions are unique, independent of any triangulation, manifestly depend only on the vertices of the underlying polytope, and can be used to easily derive identities amongst different triangulations. As one application of this formalism, we obtain new expressions for the volume of the tree-level, n-point NMHV dual amplituhedron.http://link.springer.com/article/10.1007/JHEP10(2017)071Scattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Michael Enciso Volumes of polytopes without triangulations Journal of High Energy Physics Scattering Amplitudes Supersymmetric Gauge Theory |
| title | Volumes of polytopes without triangulations |
| title_full | Volumes of polytopes without triangulations |
| title_fullStr | Volumes of polytopes without triangulations |
| title_full_unstemmed | Volumes of polytopes without triangulations |
| title_short | Volumes of polytopes without triangulations |
| title_sort | volumes of polytopes without triangulations |
| topic | Scattering Amplitudes Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP10(2017)071 |
| work_keys_str_mv | AT michaelenciso volumesofpolytopeswithouttriangulations |