Nuclear Physics B219 (1983) 513-523 © North-Holland Publishing Company GAUGE SETS AND THE 1/N EXPANSION E. CIAPESSONI and G. M. CICUTA [stituto di Fisica, Universit~Jdi Milano and [stituto Nazionale di Fisica Nucleare, Mi[ano, Italy Received 18 November 1982 All the linearly independent gauge-invariant relations, up to order ten in the coupling constant, are obtained as coefficients of the I/N expansion in a generic non-abelian gauge theory. The large-order expansion of the group SO(N) × U(I) is the most effective tool. 1. Introduction In a recent paper [1] the gauge invariant structure of a generic non-abelian gauge theory was analysed and it was shown that the whole perturbation expansion of the theory may be subdivided into separate gauge invariant sectors. These sectors seem to have relevance for the dynamics of the theory, since there are indications that infrared cancellations and exponentiations or high energy exponentiations do occur within these sectors. The method of the proof was also interesting: rather than look for cancellations of gauge dependent contributions in the space-time factors of a set of Feynman graphs, the authors studied the group theoretic factors, called color weights. These weights were considered as elements of an abstract vector space and the Lie algebra relation [T i, ~] = iCi.ikTa, (1.1) allows to express all color weights involving three-gluon coupling or four-gluon coupling as linear combinations of color weights without gluon self-coupling, that is graphs that look like quantum electrodynamics graphs of the same order in the coupling constant. Furthermore the same Lie algebra relation (1.1) induces linear relations among the color weights of QED-like graphs at fixed order in the coupling constant. It is then possible to express all color weights as linear combinations of a subset, say {Gj} of the color weights of QED-like graphs, called the color basis. The contribution of a generic term G of the perturbative series may be written as A~, = VV~;C(;FG., (1.2) 513