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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SpringerOpen
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)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. |
| format | Article |
| id | doaj-art-2ec16ea41110455faf82e239aaca4ae6 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| 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 |
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