1. All-loop group-theory constraints for four-point amplitudes of SU($N$), SO($N$), and Sp($N$) gauge theories
- Author
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Naculich, Stephen G. and Osathapan, Athis
- Subjects
High Energy Physics - Theory ,High Energy Physics - Phenomenology - 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 $L \ge 2$) 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., Comment: 46 pages, 1 figure; v2: paragraph added to conclusions, published version
- Published
- 2024