Study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon

Journal Article · Wed Nov 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.74.105007· OSTI ID:20864149

Capri, M A. L.; Lemes, V E. R.; Sobreiro, R F; Sorella, S P; Thibes, R ^[1]

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1. UERJ, Universidade do Estado do Rio de Janeiro, Rua Sao Francisco Xavier 524, 20550-013 Maracana, Rio de Janeiro (Brazil)

We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z{sub g}Z{sub A}{sup 1/2}=1, relating the renormalization factors of the gauge coupling constant Z{sub g} and of the diagonal gluon field Z{sub A}, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.

• OSTI ID: 20864149
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 74; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANOMALOUS DIMENSION
APPROXIMATIONS
COUPLING CONSTANTS
EUCLIDEAN SPACE
GLUONS
QUANTUM FIELD THEORY
RENORMALIZATION
SU-2 GROUPS
U-1 GROUPS
WARD IDENTITY
YANG-MILLS THEORY