English

The Many Colours of Amplitudes

High Energy Physics - Theory 2024-12-31 v1 Representation Theory

Abstract

We study the colour-dependence of scattering amplitudes in Yang-Mills theory with arbitrary (but fixed) gauge group and various representations of charged matter. When the rank of the gauge theory is taken arbitrarily large compared to the number of particles involved in an amplitude, it is well known that the number of independent colour-structure tensors grows factorially with multiplicity; however, for any fixed gauge group, this number grows at most exponentially with multiplicity. We review how this counting arises in representation theory and survey its implications for a wide variety of specific gauge groups with various representations of charged matter, uncovering several surprising structures along the way.

Keywords

Cite

@article{arxiv.2412.21189,
  title  = {The Many Colours of Amplitudes},
  author = {Jacob L. Bourjaily and Michael Plesser and Cristian Vergu},
  journal= {arXiv preprint arXiv:2412.21189},
  year   = {2024}
}

Comments

50 pages, 26 figures, 17 tables. Numbers of independent tensors for n-adjoint scattering for algebras through rank 8 provided as an ancillary file

R2 v1 2026-06-28T20:52:36.753Z