The method of 1/N-expansion can be applied to QCD. This was done by 't Hooft [Hoo74a] using the inverse number of colors for the gauge group SU(N) as an expansion parameter.

For an SU(N) gauge theory without virtual quark loops, the expansion goes in 1/N2 and rearranges diagrams of perturbation theory according to their topology. The leading order in 1/N2 is given by planar diagrams, which have the topology of a sphere, while the expansion in 1/N2 plays the role of a topological expansion. This is similar to an expansion in the string coupling constant in string models of the strong interaction, which also has a topological character.

Virtual quark loops can be easily incorporated in the 1/N-expansion. One distinguishes between the 't Hooft limit when the number of quark flavors Nf is fixed as N → ∞ and the Veneziano limit [Ven76] when the ratio Nf/N is fixed as N → ∞. Virtual quark loops are suppressed in the 't Hooft limit as 1/N and lead in the Veneziano limit to the same topological expansion as dual-resonance models of strong interaction.

The simplification of QCD in the large-N limit arises from the fact that the number of planar graphs grows with the number of vertices only exponentially rather than factorially as do the total number of graphs. Correlators of gauge-invariant operators factorize in the large-N limit, which looks like the leading-order term of a “semiclassical” WKB-expansion in 1/N.