Analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge

D. Dudal, J. A. Gracey, V. E. R. Lemes, M. S. Sarandy, R. F. Sobreiro, S. P. Sorella, and H. Verschelde

Phys. Rev. D 70, 114038 – Published 30 December 2004

Abstract

We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in $S U (N)$ Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate $⟨ A_{μ}^{2} ⟩$ , which has attracted much attention in the Landau gauge.

Received 16 June 2004

DOI:https://doi.org/10.1103/PhysRevD.70.114038

Authors & Affiliations

D. Dudal^1,*, J. A. Gracey^2,†, V. E. R. Lemes^3,‡, M. S. Sarandy^4,§, R. F. Sobreiro^3,∥, S. P. Sorella^3,¶, and H. Verschelde^1,**

¹Ghent University, Department of Mathematical Physics and Astronomy, Krijgslaan 281-S9, B-9000 Gent, Belgium
²Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P. O. Box 147, Liverpool, L69 3BX, United Kingdom
³UERJ—Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Maracanã, Rio de Janeiro, Brazil
⁴Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada

^*Research Assistant of the Fund for Scientific Research-Flanders (Belgium) Electronic address: david.dudal@ugent.be
^†Electronic address: jag@amtp.liv.ac.uk
^‡Electronic address: vitor@dft.if.uerj.br
^§Electronic address: msarandy@chem.utoronto.ca
^∥Electronic address: sobreiro@uerj.br
^¶Electronic address: sorella@uerj.br
^**Electronic address: henri.verschelde@ugent.be

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Vol. 70, Iss. 11 — 1 December 2004

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