Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills
Abstract
We construct a BRST-exact quartet mechanism in SU(3) Yang-Mills theory in the Landau gauge. The quartet sector is cohomologically trivial in the standard vacuum, ensuring equivalence to pure Yang-Mills theory, and its transformation rules carry both commutator and anticommutator structures, enlarging the field content from eight to nine degrees of freedom. The quartet prepotential is oriented by an auxiliary adjoint field 𝒩3 of mass dimension two (the Cartan spurion) through a BRST-exact term, and the spurion sector is closed by a perfect-square potential λ1Tr[(𝒩3−μ2T3)2], whose seed μ2T3 is the unique external scale of the model. As an algebraic quantum field with covariant BRST law s𝒩3=ig[𝒩3,c], 𝒩3 keeps the counterterm space finite by power counting. The coupled classical field equations admit an exact stationary solution ⟨𝒩3⟩=μ2effT3, around which the gauge fields acquire a mass matrix proportional to d3ab only, reproducing the i-particle propagator structure of earlier replica models without explicit breaking terms: a massless (1,2) sector and complex-conjugate poles in the (4,5), (6,7) and diagonalized (3,8) sectors. To respect the BRST doublet theorem, we separate background generation from observable cohomology. Introducing a background-equivariant covariant Cartan frame, we show that the filtered i-particle bilinear is the lowest component of an all-orders off-shell BRST cocycle. At one loop, its two-point function admits a Kallen-Lehmann representation with a real positive threshold and positive spectral density, despite the complex poles of the elementary propagators. The fully quantized action provides a consistent starting point for algebraic renormalization.
Versions
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BibTeX
@misc{amaral2026backgroundequivariant,
title = {{Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills}},
author = {M. M. Amaral and V. E. R. Lemes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.16172},
eprint = {2605.16172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16172},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills
AU - M. M. Amaral
AU - V. E. R. Lemes
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2605.16172
UR - https://arxiv.org/abs/2605.16172
AB - We construct a BRST-exact quartet mechanism in SU(3) Yang-Mills theory in the Landau gauge. The quartet sector is cohomologically trivial in the standard vacuum, ensuring equivalence to pure Yang-Mills theory, and its transformation rules carry both commutator and anticommutator structures, enlarging the field content from eight to nine degrees of freedom. The quartet prepotential is oriented by an auxiliary adjoint field 𝒩_3 of mass dimension two (the Cartan spurion) through a BRST-exact term, and the spurion sector is closed by a perfect-square potential λ_1Tr[(𝒩_3−μ^2T^3)^2], whose seed μ^2T^3 is the unique external scale of the model. As an algebraic quantum field with covariant BRST law s𝒩_3=ig[𝒩_3,c], 𝒩_3 keeps the counterterm space finite by power counting. The coupled classical field equations admit an exact stationary solution ⟨𝒩_3⟩=μ^2_effT^3, around which the gauge fields acquire a mass matrix proportional to d^3ab only, reproducing the i-particle propagator structure of earlier replica models without explicit breaking terms: a massless (1,2) sector and complex-conjugate poles in the (4,5), (6,7) and diagonalized (3,8) sectors. To respect the BRST doublet theorem, we separate background generation from observable cohomology. Introducing a background-equivariant covariant Cartan frame, we show that the filtered i-particle bilinear is the lowest component of an all-orders off-shell BRST cocycle. At one loop, its two-point function admits a Kallen-Lehmann representation with a real positive threshold and positive spectral density, despite the complex poles of the elementary propagators. The fully quantized action provides a consistent starting point for algebraic renormalization.
ER -