Color symmetry in the large-nlimit

We investigate the selection of certain dominant topological classes of Feynman diagrams in the large-$n$ limit in the context of a non-Abelian gauge field theory, where the nontrivial couplings of the regular representation of the group are involved. We find that nonplanar diagrams are suppressed relative to locally planar diagrams by factors of $\frac{1}{n^2}$ in the case of $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ and by factors of $\frac{1}{n}$ in the case of $\mathrm{SO}\mathrm{}\left(n\right)\mathrm{}$ or $\mathrm{Sp}\mathrm{}\left(n\right)\mathrm{}$. We consider the concrete example of the meson bound states in a theory of colored quarks bound by colored gauge vector gluons, where the topological selection corresponds to that required for hadrons in a dual theory.