Revealing the landscape of globally color-dual multi-loop integrands
Abstract We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing D-dimensional co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2024)163 |
| _version_ | 1827205534885871616 |
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| author | Alex Edison James Mangan Nicolas H. Pavao |
| author_facet | Alex Edison James Mangan Nicolas H. Pavao |
| author_sort | Alex Edison |
| collection | DOAJ |
| description | Abstract We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing D-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use a D-dimensional color-dual bootstrap to successfully construct globally color-dual local two-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and $$\mathcal{N}$$ = 4 super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order. |
| first_indexed | 2024-04-24T12:43:23Z |
| format | Article |
| id | doaj.art-31a83543633744f99d1c858252cbe6ad |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T12:09:49Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-31a83543633744f99d1c858252cbe6ad2024-06-30T11:08:08ZengSpringerOpenJournal of High Energy Physics1029-84792024-03-012024314010.1007/JHEP03(2024)163Revealing the landscape of globally color-dual multi-loop integrandsAlex Edison0James Mangan1Nicolas H. Pavao2Department of Physics and Astronomy, Northwestern UniversityDepartment of Physics and Astronomy, Northwestern UniversityDepartment of Physics and Astronomy, Northwestern UniversityAbstract We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructing D-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use a D-dimensional color-dual bootstrap to successfully construct globally color-dual local two-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and $$\mathcal{N}$$ = 4 super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order.https://doi.org/10.1007/JHEP03(2024)163Scattering AmplitudesDuality in Gauge Field TheoriesEffective Field Theories |
| spellingShingle | Alex Edison James Mangan Nicolas H. Pavao Revealing the landscape of globally color-dual multi-loop integrands Journal of High Energy Physics Scattering Amplitudes Duality in Gauge Field Theories Effective Field Theories |
| title | Revealing the landscape of globally color-dual multi-loop integrands |
| title_full | Revealing the landscape of globally color-dual multi-loop integrands |
| title_fullStr | Revealing the landscape of globally color-dual multi-loop integrands |
| title_full_unstemmed | Revealing the landscape of globally color-dual multi-loop integrands |
| title_short | Revealing the landscape of globally color-dual multi-loop integrands |
| title_sort | revealing the landscape of globally color dual multi loop integrands |
| topic | Scattering Amplitudes Duality in Gauge Field Theories Effective Field Theories |
| url | https://doi.org/10.1007/JHEP03(2024)163 |
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