LESSONS FROM 2-DIMENSIONAL QCD (N--]INFINITY) - VACUUM-STRUCTURE, ASYMPTOTIC SERIES, INSTANTONS, AND ALL THAT

Authors
Citation
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
Citations number
50
Categorie Soggetti
Physics, Particles & Fields
ISSN journal
05562821
Volume
53
Issue
10
Year of publication
1996
Pages
5821 - 5833
Database
ISI
SICI code
0556-2821(1996)53:10<5821:LF2Q(->2.0.ZU;2-H
Abstract
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.