Abstract

We establish the quantum consistency of the Axis Model, a geometric framework in which the Standard Model gauge sectors emerge from scalar-stabilized internal vector degrees of freedom. At the effective-field-theory level the model is formulated in terms of a complex scalar coherence field Φ, a massive gravitational vector Gμ associated with an internal U (1)G, and a massless spatial vector Xμ (the composite-photon carrier), coupled to chiral fermions; the underlying tri-vector morton structure appears only in the geometric interpretation of these fields. We derive the gauge-invariant operator content via projection geometry, construct a BRST-invariant action (with Stückelberg realization of the massive Gμ sector), and demonstrate perturbative unitarity and ghost cancellation. Anomaly cancellation is shown to follow from scalar-bundle triviality, c1(Φ) = 0, which enforces vanishing of all triangle anomaly coefficients without ad hoc charge assignments. A two-loop renormalization-group analysis shows that the scalar vacuum remains stable (λ(μ) > 0) and all couplings stay perturbative throughout the Axis EFT window EIR < μ < ΛΦ < Λq, where ΛΦ ∼ 105 GeV is the scalar-coherence cutoff and Λq ∼ 1016 GeV marks the matching scale to the pre-geometric parent theory. Within this window the low-energy limit reproduces the Standard Model gauge sector, and the Abelian U(1)G Landau pole is safely avoided by matching at Λq . These results demonstrate that the Axis Model admits a rigorous, unitary, and radiatively stable quantum realization compatible with Standard Model phenomenology.

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Keywords: Unified Field Theory, Scalar field, anomaly cancellation, BRST quantization, effective field theory, Standard Model, renormalization group, gauge symmetry, quantum field theory, internal geometry, electroweak unification.