Lessons from two-dimensional QCD (N→∞): Vacuum structure, asymptotic series, instantons, and all that

We discuss two-dimensional QCD (Nc→∞) with fermions in the fundamental as well as adjoint representation. We find factorial growth ∼(g2Ncπ)2k(2k)exclamation point(-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 heavy-light quark system Q bar q within the operator product expansion (which turns out to be an asymptotic series). Some vacuum condensates left-angle bar q(xμDμ)2nq right-angle ∼(x2)nn exclamation point which are responsible for this factorial growth are also discussed. We formulate some general puzzles which are not specific for two-dimensional physics, but are inevitable features of any asymptotic expansion. We resolve these apparent puzzles within two-dimensional QCD and we speculate that analogous puzzles might occur in real four-dimensional QCD as well. copyright 1996 The American Physical Society