ar X iv : h ep - p h / 95 10 36 6 v 2 6 M ar 1 99 6 Lessons from QCD 2 ( N → ∞ ) : Vacuum structure , Asymptotic Series ,

We discuss two dimensional QCD(Nc → ∞) with fermions in the fundamental as well as adjoint representation. We find factorial growth ∼ (gNcπ) (2k)!(−1) k−1 (2π)2k in the coefficients of the large order perturbative expansion. We argue that this behavior is related to classical solutions of the theory, instantons, thus it has nonperturbative origin. Phenomenologically such a growth is related to highly excited states in the spectrum. We also analyze the heavylight quark system Qq̄ within operator product expansion (which it turns out to be an asymptotic series). Some vacuum condensates 〈q̄(xμDμ)q〉 ∼ (x2)n · n! which are responsible for this factorial growth are also discussed. We formulate some general puzzles which are not specific for 2D physics, but are inevitable features of any asymptotic expansion. We resolve these apparent puzzles within QCD2 and we speculate that analogous puzzles might occur in real 4-dimensional QCD as well. 1 e-mail address:[email protected]