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