Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity
The biadjoint scalar theory has cubic interactions and fields transforming in the biadjoint representation of SU() × SU(Ñ). Amplitudes are ''color'' decomposed in terms of partial amplitudes computed using Feynman diagrams, which are simultaneously planar with respect to two orde...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212107 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity. Freddy Cachazo, Nick Early and Yong Zhang. SIGMA 20 (2024), 016, 44 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720422122881024 |
|---|---|
| author | Cachazo, Freddy Early, Nick Zhang, Yong |
| author_facet | Cachazo, Freddy Early, Nick Zhang, Yong |
| citation_txt | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity. Freddy Cachazo, Nick Early and Yong Zhang. SIGMA 20 (2024), 016, 44 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The biadjoint scalar theory has cubic interactions and fields transforming in the biadjoint representation of SU() × SU(Ñ). Amplitudes are ''color'' decomposed in terms of partial amplitudes computed using Feynman diagrams, which are simultaneously planar with respect to two orderings. In 2019, a generalization of biadjoint scalar amplitudes based on generalized Feynman diagrams (GFDs) was introduced. GFDs are collections of Feynman diagrams derived by incorporating an additional constraint of ''local planarity'' into the construction of the arrangements of metric trees in combinatorics. In this work, we propose a natural generalization of color orderings that leads to color-dressed amplitudes. A generalized color ordering (GCO) is defined as a collection of standard color orderings that is induced, in a precise sense, from an arrangement of projective lines on ℝℙ². We present results for ≤ 9 generalized color orderings and GFDs, uncovering new phenomena in each case. We discover generalized decoupling identities and propose a definition of the ''colorless'' generalized scalar amplitude. We also propose a notion of GCOs for arbitrary ℝℙᵏ⁻¹, discuss some of their properties, and comment on their GFDs. In a companion paper, we explore the definition of partial amplitudes using CEGM integral formulas.
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| first_indexed | 2026-03-21T02:33:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212107 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T02:33:06Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cachazo, Freddy Early, Nick Zhang, Yong 2026-01-28T13:55:54Z 2024 Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity. Freddy Cachazo, Nick Early and Yong Zhang. SIGMA 20 (2024), 016, 44 pages 1815-0659 2020 Mathematics Subject Classification: 14M15; 05E99; 14T99 arXiv:2212.11243 https://nasplib.isofts.kiev.ua/handle/123456789/212107 https://doi.org/10.3842/SIGMA.2024.016 The biadjoint scalar theory has cubic interactions and fields transforming in the biadjoint representation of SU() × SU(Ñ). Amplitudes are ''color'' decomposed in terms of partial amplitudes computed using Feynman diagrams, which are simultaneously planar with respect to two orderings. In 2019, a generalization of biadjoint scalar amplitudes based on generalized Feynman diagrams (GFDs) was introduced. GFDs are collections of Feynman diagrams derived by incorporating an additional constraint of ''local planarity'' into the construction of the arrangements of metric trees in combinatorics. In this work, we propose a natural generalization of color orderings that leads to color-dressed amplitudes. A generalized color ordering (GCO) is defined as a collection of standard color orderings that is induced, in a precise sense, from an arrangement of projective lines on ℝℙ². We present results for ≤ 9 generalized color orderings and GFDs, uncovering new phenomena in each case. We discover generalized decoupling identities and propose a definition of the ''colorless'' generalized scalar amplitude. We also propose a notion of GCOs for arbitrary ℝℙᵏ⁻¹, discuss some of their properties, and comment on their GFDs. In a companion paper, we explore the definition of partial amplitudes using CEGM integral formulas. The authors thank B. Schroeter, B. Sturmfels, and B. Umbert for useful correspondence and discussions. This research was supported in part by a grant from the Gluskin Sheff/Onex Freeman Dyson Chair in Theoretical Physics and by Perimeter Institute. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This research received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 725110), Novel structures in scattering amplitudes. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity Article published earlier |
| spellingShingle | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity Cachazo, Freddy Early, Nick Zhang, Yong |
| title | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity |
| title_full | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity |
| title_fullStr | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity |
| title_full_unstemmed | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity |
| title_short | Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity |
| title_sort | color-dressed generalized biadjoint scalar amplitudes: local planarity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212107 |
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