Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory
Abstract The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In...
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2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)124 |
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| author | Zhenjie Li |
| author_facet | Zhenjie Li |
| author_sort | Zhenjie Li |
| collection | DOAJ |
| description | Abstract The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3, ζ 5 to the cusp anomalous dimension. |
| format | Article |
| id | doaj-art-3853a8a942fc4063b551acf9ff3a20a5 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-3853a8a942fc4063b551acf9ff3a20a52024-12-08T12:10:21ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241012610.1007/JHEP10(2024)124Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theoryZhenjie Li0SLAC National Accelerator Laboratory, Stanford UniversityAbstract The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3, ζ 5 to the cusp anomalous dimension.https://doi.org/10.1007/JHEP10(2024)124Scattering AmplitudesChern-Simons TheoriesWilson’t Hooft and Polyakov loopsSupersymmetric Gauge Theory |
| spellingShingle | Zhenjie Li Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory Journal of High Energy Physics Scattering Amplitudes Chern-Simons Theories Wilson ’t Hooft and Polyakov loops Supersymmetric Gauge Theory |
| title | Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory |
| title_full | Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory |
| title_fullStr | Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory |
| title_full_unstemmed | Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory |
| title_short | Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory |
| title_sort | integrating the full four loop negative geometries and all loop ladder type negative geometries in abjm theory |
| topic | Scattering Amplitudes Chern-Simons Theories Wilson ’t Hooft and Polyakov loops Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP10(2024)124 |
| work_keys_str_mv | AT zhenjieli integratingthefullfourloopnegativegeometriesandallloopladdertypenegativegeometriesinabjmtheory |