All-loop group-theory constraints for four-point amplitudes of SU($N$), SO($N$), and Sp($N$) gauge theories
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| Format: | Preprint |
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2024
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| _version_ | 1866912100457119744 |
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| author | Naculich, Stephen G. Osathapan, Athis |
| author_facet | Naculich, Stephen G. Osathapan, Athis |
| contents | 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 $L \ge 2$) and for SO($N$) and Sp($N$), we establish the existence of seventeen independent null vectors (for $L \ge 5$). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_03403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All-loop group-theory constraints for four-point amplitudes of SU($N$), SO($N$), and Sp($N$) gauge theories Naculich, Stephen G. Osathapan, Athis High Energy Physics - Theory High Energy Physics - Phenomenology 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 $L \ge 2$) and for SO($N$) and Sp($N$), we establish the existence of seventeen independent null vectors (for $L \ge 5$). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory. |
| title | All-loop group-theory constraints for four-point amplitudes of SU($N$), SO($N$), and Sp($N$) gauge theories |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2407.03403 |