Lessons from two-dimensional QCD ({ital N}{r_arrow}{infinity}): Vacuum structure, asymptotic series, instantons, and all that

Journal Article · Wed May 01 04:00:00 EDT 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.5821· OSTI ID:284020

Zhitnitsky, A R ^[1]

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1. Physics Department, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, V6T 1Z1 (CANADA)

We discuss two-dimensional QCD ({ital N}{sub {ital c}}{r_arrow}{infinity}) with fermions in the fundamental as well as adjoint representation. We find factorial growth {approximately}({ital g}{sup 2}{ital N}{sub {ital c}}{pi}){sup 2{ital k}}(2{ital k})!({minus}1){sup {ital k}{minus}1}/(2{pi}){sup 2{ital k}} 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 {ital Q{bar q}} within the operator product expansion (which turns out to be an asymptotic series). Some vacuum condensates {l_angle}{bar {ital q}}({ital x}{sub {mu}}{ital D}{sub {mu}}){sup 2{ital n}}{ital q}{r_angle}{approximately}({ital x}{sup 2}){sup {ital nn}}! 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} {ital 1996 The American Physical Society.}

• OSTI ID: 284020
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 10 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ASYMPTOTIC SOLUTIONS
CONDENSATES
EXCITED STATES
FERMIONS
INSTANTONS
OPERATOR PRODUCT EXPANSION
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
QUARKS
SPECTRA
TWO-DIMENSIONAL CALCULATIONS
VACUUM STATES