Compositeness condition for non-abelian gauge fields

We derive and solve the compositeness condition for the SU(N-c) gauge boson at the next-to-leading order in 1/N-f(N-f is the number of flavors) and th e leading order in In Lambda(2) (Lambda is the compositeness scale) to obta in an expression for the gauge coupling constant in terms of the compositen ess scale. It turns out that the gauge-boson compositeness (with a large La mbda) takes place only when N-f/N-c > 11/2, in which the asymptotic freedom fails. (C) 1998 Elsevier Science B.V. All rights reserved.