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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Main Author: Zhenjie Li
Format: Article
Language:English
Published: SpringerOpen 2024-10-01
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.
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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