Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills

TL;DR

This paper develops a BRST-exact quartet framework in SU(3) Yang-Mills theory, enabling the construction of i-particle propagators with a consistent, renormalizable quantum action.

Contribution

It introduces a novel BRST quartet mechanism in SU(3) Yang-Mills theory that reproduces i-particle propagator structures without explicit symmetry breaking.

Findings

Reproduces i-particle propagator structure in a BRST-invariant manner

Maintains a positive spectral density despite complex poles

Provides a systematic, renormalizable framework for observable construction

Abstract

In this work, 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. The transformation rules carry both commutator and anticommutator structures, enlarging the field content from eight to nine degrees of freedom. Working in a prescribed Cartan-oriented background (compatible with the classical equations of motion), the theory induces a mass matrix reproducing the distinct $i$-particle propagator structure of earlier replica models without explicit breaking terms. To respect the BRST doublet theorem, we separate background generation from observable cohomology. Introducing a background-equivariant covariant Cartan frame, we show the filtered $i$-particle bilinear is the lowest perturbative component of an all-orders off-shell BRST cocycle. Despite the complex poles of elementary propagators, its leading two-point function retains a K\"all\'en--Lehmann representation with a real positive threshold and positive spectral density. The fully quantized action provides a consistent framework for renormalizability, establishing a systematic mechanism for recovering $i$-particle propagators and identifying BRST-controlled composite observables from a BRST-exact quartet extended to $SU(3)$.