Color-ordered amplitudes for higher-rank structure constants

Determine whether a well-defined notion of color-ordered partial amplitudes exists for theories built from totally antisymmetric higher-rank structure constants f^{abc\ldots}.

Background

Color ordering is central to organizing amplitudes in ordinary gauge theories, where structure constants can be related to traces of generators. The paper notes that the higher-rank objects considered here are not generally constructed from such traces.

A suitable color-ordering prescription would provide the basis for defining partial amplitudes and could enable further amplitude relations analogous to those known in adjoint gauge theory.

References

Is there a notion of color-ordered partial amplitudes?

— Color Relations and Off-Shell Double-Copy for Towers of Theories  (2609.36604 - Mangan et al., 29 Sep 2026) in Section 4, Conclusions and future directions

If a suitable version of color-ordering is found, are there KLT relations , fundamental BCJ identities , or Kleiss-Kuijf relations ?

— Color Relations and Off-Shell Double-Copy for Towers of Theories  (2609.36604 - Mangan et al., 29 Sep 2026) in Section 4, Conclusions and future directions

If fundamental BCJ relations are found in the $n$-index case, does the theory have hidden zeroes ?

— Color Relations and Off-Shell Double-Copy for Towers of Theories  (2609.36604 - Mangan et al., 29 Sep 2026) in Section 4, Conclusions and future directions