Ultraviolet divergences in 1/N expansions of asymptotically free theories

Journal Article · Mon Oct 15 00:00:00 EDT 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.30.1763· OSTI ID:6044532

Rim, C; Weisberger, W I

We calculate the ultraviolet divergences of the nonlinear sigma and Gross-Neveu models in the 1/N expansion near two dimensions (d = 2-epsilon). Beyond the leading order the theories develop logarithmic as well as pole singularities in epsilon. Identical divergences occur when the renormalization constants calculated in perturbation theory are expanded in powers of 1/N rather than in powers of the coupling constants. The necessary infinite renormalizations of the 1/N expansions are completely determined by the two-loop ..beta.. functions and one-loop anomalous dimensions of perturbation theory. These results can be extended to non-Abelian gauge theories in four dimensions which admit 1/N expansions.

• Research Organization: Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3840
• OSTI ID: 6044532
• Journal Information: Phys. Rev. D; (United States), Vol. 30:8
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SIGMA MODEL
ULTRAVIOLET DIVERGENCES
CHIRAL SYMMETRY
COUPLING CONSTANTS
GAUGE INVARIANCE
GREEN FUNCTION
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
RENORMALIZATION
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
SYMMETRY
645400* - High Energy Physics- Field Theory