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 ${\mathcal{N}}_3$ of mass dimension two (the Cartan spurion) through a BRST-exact term, and the spurion sector is closed by a perfect-square potential ${\lambda }_1\mathrm{Tr}[({\mathcal{N}}_3-{\mu }^2{T}^3{)}^2]$, whose seed ${\mu }^2{T}^3$ is the unique external scale of the model. As an algebraic quantum field with covariant BRST law $s{\mathcal{N}}_3=ig[{\mathcal{N}}_3,c]$, ${\mathcal{N}}_3$ keeps the counterterm space finite by power counting. The coupled classical field equations admit an exact stationary solution $⟨{\mathcal{N}}_3⟩={\mu }_{\mathrm{eff}}^2{T}^3$, 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.

27 pages, nofigures