Abstract (Elsevier)
A gauge theory with colour gauge group U( N ) and quarks having a colour index running from one to N is considered in the limit N → ∞, g 2 N fixed. It is shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/ N is identical to that of the dual models, such that the number 1/ N corresponds to the dual coupling constant. For hadrons N is probably equal to three. A mathematical framework is proposed to link these concepts of planar diagrams with the functional integrals of Gervais, Sakita and Mandelstam for the dual string.