All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories

Abstract In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an i...

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Main Authors: Stephen G. Naculich, Athis Osathapan
Format: Article
Language:English
Published: SpringerOpen 2024-10-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP10(2024)221
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author Stephen G. Naculich
Athis Osathapan
author_facet Stephen G. Naculich
Athis Osathapan
author_sort Stephen G. Naculich
collection DOAJ
description Abstract In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an iterative process, we systematically construct the L-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (for L ≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (for L ≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.
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spelling doaj-art-2ec16ea41110455faf82e239aaca4ae62025-08-20T02:20:38ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241014310.1007/JHEP10(2024)221All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theoriesStephen G. Naculich0Athis Osathapan1Department of Physics and Astronomy, Bowdoin CollegeDepartment of Physics and Astronomy, Bowdoin CollegeAbstract In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an iterative process, we systematically construct the L-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (for L ≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (for L ≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.https://doi.org/10.1007/JHEP10(2024)2211/N ExpansionDuality in Gauge Field TheoriesGauge SymmetryScattering Amplitudes
spellingShingle Stephen G. Naculich
Athis Osathapan
All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
Journal of High Energy Physics
1/N Expansion
Duality in Gauge Field Theories
Gauge Symmetry
Scattering Amplitudes
title All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
title_full All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
title_fullStr All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
title_full_unstemmed All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
title_short All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories
title_sort all loop group theory constraints for four point amplitudes of su n so n and sp n gauge theories
topic 1/N Expansion
Duality in Gauge Field Theories
Gauge Symmetry
Scattering Amplitudes
url https://doi.org/10.1007/JHEP10(2024)221
work_keys_str_mv AT stephengnaculich allloopgrouptheoryconstraintsforfourpointamplitudesofsunsonandspngaugetheories
AT athisosathapan allloopgrouptheoryconstraintsforfourpointamplitudesofsunsonandspngaugetheories