Vacuum condensate in (2+1)-dimensional gauge theories

Journal Article · Mon Jul 15 00:00:00 EDT 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.44.464· OSTI ID:5727775

Trottier, H D ^[1]

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1. Physics Department, McGill University, 3600 University St., Montreal, Quebec, Canada H3A2T8 (CA)

The one-loop effective potential for a background field in (2+1)-dimensional SU({ital N}) gauge theory is calculated at arbitrary temperature. The perturbative vacuum is found to be unstable against spontaneous formation of a gauge-field condensate at zero temperature, corresponding to a nontrivial minimum of the effective potential. The condensate is found to evaporate'' at a first-order phase transition---above a critical temperature {ital T}{sub {ital c}}, the minimum of the free energy lies at a zero background field. The condensate also vanishes for a sufficiently large number of massless fermions. These properties of the gauge-field effective potential are shown to provide a mean-field description of interacting charges in 2+1 dimensions that exhibits {ital linear} confinement (to be compared with a logarithmic interaction in the purely classical theory), and a first-order ( deconfining'') phase transition. Similar qualitative features have been found in the one-loop effective potential for (3+1)-dimensional gauge theories.

• OSTI ID: 5727775
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 44:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ELECTRODYNAMICS
ENERGY
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FREE ENERGY
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
MEAN-FIELD THEORY
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
QUANTUM CHROMODYNAMICS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SPACE-TIME
SU GROUPS
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
VACUUM STATES