Positive Configuration Space
Abstract We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a po...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/136768 |
| _version_ | 1811080184791564288 |
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| author | Arkani-Hamed, Nima Lam, Thomas Spradlin, Marcus |
| author_facet | Arkani-Hamed, Nima Lam, Thomas Spradlin, Marcus |
| author_sort | Arkani-Hamed, Nima |
| collection | MIT |
| description | Abstract
We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. Our work is motivated by connections to super Yang–Mills scattering amplitudes, which will be discussed in a sequel. |
| first_indexed | 2024-09-23T11:27:12Z |
| format | Article |
| id | mit-1721.1/136768 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:27:12Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1367682021-11-02T03:27:50Z Positive Configuration Space Arkani-Hamed, Nima Lam, Thomas Spradlin, Marcus Abstract We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space. This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. Our work is motivated by connections to super Yang–Mills scattering amplitudes, which will be discussed in a sequel. 2021-11-01T14:33:14Z 2021-11-01T14:33:14Z 2021-04-11 2021-04-18T03:14:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136768 PUBLISHER_CC en https://doi.org/10.1007/s00220-021-04041-x Creative Commons Attribution The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Arkani-Hamed, Nima Lam, Thomas Spradlin, Marcus Positive Configuration Space |
| title | Positive Configuration Space |
| title_full | Positive Configuration Space |
| title_fullStr | Positive Configuration Space |
| title_full_unstemmed | Positive Configuration Space |
| title_short | Positive Configuration Space |
| title_sort | positive configuration space |
| url | https://hdl.handle.net/1721.1/136768 |
| work_keys_str_mv | AT arkanihamednima positiveconfigurationspace AT lamthomas positiveconfigurationspace AT spradlinmarcus positiveconfigurationspace |