Instantons and fermion condensate in adjoint two-dimensional QCD

Journal Article · Wed Jun 15 04:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.6836· OSTI ID:7308584

Smilga, A V ^[1]

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1. Theoretical Physics Institute, University of Minnesota, 116 Church St. S.E., Minneapolis, Minnesota 55455 (United States)

We show that two-dimensional QCD with adjoint fermions involves instantons due to nontrivial [pi][sub 1][SU([ital N])/[ital Z][sub [ital N]]]=[ital Z][sub [ital N]]. At high temperatures, the quasiclassical approximation works and the action and the form of the effective (with account of quantum corrections) instanton solution can be evaluated. The instanton presents a localized configuration with a size [proportional to][ital g][sup [minus]1]. At [ital N]=2, it involves exactly 2 zero fermion modes and gives rise to the fermion condensate [l angle][bar [lambda]][sup [ital a]][lambda][sup [ital a]][r angle][sub [ital T]] which falls off [proportional to]exp[l brace][minus][pi][sup 3/2][ital T]/[ital g][r brace] at high [ital T] but remains finite. At low temperatures, both instanton and bosonization arguments also exhibit the appearance of the fermion condensate [l angle][bar [lambda]][sup [ital a]][lambda][sup [ital a]][r angle][sub [ital T]=0][similar to][ital g]. For [ital N][gt]2, the situation is paradoxical. There are 2([ital N][minus]1) fermion zero modes in the instanton background which implies the absence of the condensate in the massless limit. On the other hand, bosonization arguments suggest the appearance of the condensate for any [ital N]. Possible ways to resolve this paradox (which occurs also in some four-dimensional gauge theories) are discussed.

• OSTI ID: 7308584
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:12; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662230 -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONDENSATES
FERMIONS
FIELD THEORIES
INSTANTONS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUASI PARTICLES
TEMPERATURE DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS