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Gribov horizon and spontaneous BRST symmetry breaking

David Dudal*

Silvio Paolo Sorella†

  • Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium

  • UERJ—Universidade do Estado do Rio de Janeiro, Instituto de Física, Departamento de Física Teórica, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro, Rio de Janeiro 20550-013, Brasil

  • *david.dudal@ugent.be
  • †sorella@uerj.br
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Phys. Rev. D 86, 045005 – Published 1 August, 2012

DOI: https://doi.org/10.1103/PhysRevD.86.045005

Abstract

An equivalent formulation of the Gribov–Zwanziger theory accounting for the gauge fixing ambiguity in the Landau gauge is presented. The resulting action is constrained by a Slavnov-Taylor identity stemming from a nilpotent exact Becchi-Rouet-Stora-Tyutin (BRST) invariance which is spontaneously broken due to the presence of the Gribov horizon. This spontaneous symmetry breaking can be described in a purely algebraic way through the introduction of a pair of auxiliary fields which give rise to a set of linearly broken Ward identities. The Goldstone sector turns out to be decoupled. The underlying exact nilpotent BRST invariance allows us to employ BRST cohomology tools within the Gribov horizon to identify renormalizable extensions of gauge invariant operators. Using a simple toy model and appropriate Dirac bracket quantization, we discuss the time evolution invariance of the operator cohomology. We further comment on the unitarity issue in a confining theory, and stress that BRST cohomology alone is not sufficient to ensure unitarity, a fact that, although well known, is frequently ignored.

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Phys. Rev. D 86, 045005– Published 1 August, 2012
  • Received 21 May 2012

© 2012 American Physical Society

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