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color charge in nLab

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The charge carried by quarks and gluons in the description of the strong nuclear force via quantum chromodynamics is called color charge.

If the gauge group is SU(N) and fermions are in the fundamental representation N\mathbf{N} of dimension NN, so that N\mathbf{N} has a linear basis of NN elements, one says that these are NN colors of the given fermion particle.

Hence, more generally one could reasonably say that the “number of colors” of a given fundamental particle in gauge theory is physics synonym for the choice of linear representation of the gauge group that defines this particle.

Howard Georgi, §16 in: Lie Algebras In Particle Physics, Westview Press (1999), CRC Press (2019) [doi:10.1201/9780429499210]