Ar. Zhitnitsky, LESSONS FROM 2-DIMENSIONAL QCD (N--]INFINITY) - VACUUM-STRUCTURE, ASYMPTOTIC SERIES, INSTANTONS, AND ALL THAT, Physical review. D. Particles and fields, 53(10), 1996, pp. 5821-5833
We discuss two-dimensional QCD (N-c-->infinity) with fermions in the f
undamental as well as adjoint representation. We find factorial growth
similar to(g(2)N(c) pi)(2k)(2k)!(-1)(k-1)/(2 pi)(2k) in the coefficie
nts of the large order perturbative expansion. We argue that this beha
vior is related to classical solutions of the theory, instantons; thus
it has nonperturbative origin. Phenomenologically such a growth is re
lated to highly excited states in the spectrum. We also analyze the he
avy-light quark system Q (q) over bar within the operator product expa
nsion (which turns out to be an asymptotic series). Some vacuum conden
sates [(q) over bar(x(mu)D(mu))(2n)q]similar to(x(2))(n)n! which are r
esponsible for this factorial growth are also discussed. We formulate
some general puzzles which are not specific for two-dimensional physic
s, but are inevitable features of any asymptotic expansion. We resolve
these apparent puzzles within two-dimensional QCD and we speculate th
at analogous puzzles might occur in real four-dimensional QCD as well.