Compositeness condition for non-abelian gauge fields

We derive and solve the compositeness condition for the SU(Nc) gauge boson at the next-to-leading order in 1/Nf (Nf is the number of flavors) and the leading order in lnΛ2 (Λ is the compositeness scale) to obtain an expression for the gauge coupling constant in terms of the compositeness scale. It turns out that the gauge-boson compositeness (with a large Λ) takes place only when Nf/Nc>11/2, in which the asymptotic freedom fails.