Spontaneous symmetry breaking as a mechanism for the Gribov scale in a BRST-invariant formulation
Abstract
We propose a BRST-invariant formulation of the Gribov--Zwanziger model in the Landau gauge, in which the Gribov scale is produced by the spontaneous breaking of a scalar quartet symmetry, rather than through the explicit breaking term of the conventional construction. We show that the resulting action preserves the ghost equation of the Landau gauge and reproduces the characteristic Gribov-type gauge propagator of the original Gribov scenario, a BRST-invariant mass term of the refined type being accommodated by the same mechanism. We establish the renormalizability of the model to all orders by means of algebraic renormalization techniques, no counterterm being required outside those already present in the classical action. We further show that the condensation of the quartet leaves unchanged the cohomology through which the observables are characterized, the operator realized in the displaced vacuum having the same cohomology as that of the symmetric phase, so that the mass scale is produced at no cost in the physical content of the theory, and the construction of genuine gauge-invariant observables in the Gribov--Zwanziger setting is thereby left open to the usual cohomological methods.
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BibTeX
@misc{capri2026spontaneous,
title = {{Spontaneous symmetry breaking as a mechanism for the Gribov scale in a BRST-invariant formulation}},
author = {M. A. L. Capri and V. E. R. Lemes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00342},
eprint = {2610.00342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00342},
}
RIS
TY - UNPB
TI - Spontaneous symmetry breaking as a mechanism for the Gribov scale in a BRST-invariant formulation
AU - M. A. L. Capri
AU - V. E. R. Lemes
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00342
UR - https://arxiv.org/abs/2610.00342
AB - We propose a BRST-invariant formulation of the Gribov--Zwanziger model in the Landau gauge, in which the Gribov scale is produced by the spontaneous breaking of a scalar quartet symmetry, rather than through the explicit breaking term of the conventional construction. We show that the resulting action preserves the ghost equation of the Landau gauge and reproduces the characteristic Gribov-type gauge propagator of the original Gribov scenario, a BRST-invariant mass term of the refined type being accommodated by the same mechanism. We establish the renormalizability of the model to all orders by means of algebraic renormalization techniques, no counterterm being required outside those already present in the classical action. We further show that the condensation of the quartet leaves unchanged the cohomology through which the observables are characterized, the operator realized in the displaced vacuum having the same cohomology as that of the symmetric phase, so that the mass scale is produced at no cost in the physical content of the theory, and the construction of genuine gauge-invariant observables in the Gribov--Zwanziger setting is thereby left open to the usual cohomological methods.
ER -