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Bibliografiske detaljer
Hovedforfatter:	Alexander, David
Format:	Recurso digital
Sprog:
Udgivet:	Zenodo 2026
Fag:	gluons, SU(3) gauge symmetry, emergent gauge invariance, three-plane scaffold, Borromean junction, domain walls, colour confinement, strong coupling constant, Jackiw-Rebbi zero modes, Yang-Mills theory, operator decoupling, mass gap, Lorentzian running, strong scale
Online adgang:	https://doi.org/10.5281/zenodo.20148910
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Indholdsfortegnelse:

The SU(3) colour gauge structure of quantum chromodynamics — the eight gluons, their Yang-Mills dynamics, and the strong coupling constant — is usually postulated as a fundamental ingredient of the Standard Model. This paper derives it from the three-plane scaffold, a model in which three mutually orthogonal scalar domain walls meet at a Borromean junction. The three domain walls produce zero modes spanning a three-dimensional complex colour space. The octahedral (Oh) symmetry of the Borromean junction forces the colour density matrix to be proportional to the identity, establishing that no colour direction is preferred. The central result is that local SU(3) colour-frame invariance is not an axiom but an emergent redundancy of the low-energy effective theory. The derivation proceeds as follows. The off-diagonal colour-frame operators — composite operators that would measure the relative phase between zero modes on different walls — are shown by explicit calculation to have no massless pole. Their two-point function is a massive bubble of Jackiw-Rebbi propagators with threshold 2y_wall and no 1/p² singularity. A complete operator classification then shows that every gauge-non-invariant operator in the low-energy effective theory is gapped with threshold at least 2y_wall: off-diagonal generators (by the explicit bubble calculation), diagonal traceless generators (by decomposing into single-wall and cross-wall bubbles), higher representations (by OPE closure), and their products. No symmetry protects a massless non-singlet — SU(3) is unbroken, there is no relevant topological charge, and t'Hooft anomaly matching does not force massless coloured states. Therefore only colour singlets survive in the low-energy local algebra, and local SU(3) frame rotations are redundancies of the effective description rather than imposed symmetries. Once local SU(3) gauge invariance is established, the Yang-Mills kinetic term follows as the unique leading gauge-invariant operator in the derivative expansion. The one-loop coefficient (11/3)N_c follows from the group theory of SU(3) and closes the assumption made in the companion electroweak paper. The left-chiral projection of the adjoint colour determinant gives (11/6)N_c for the weak-sector correction, with the factor of one-half arising from the parity symmetry of the junction/anti-junction vacuum ensemble. The scaffold mechanism for emergent gauge symmetry is situated relative to known approaches: it is closest to slave-particle constructions but distinct in that the redundancy is forced by dynamics (the mass gap) rather than introduced as a calculational device. The closest structural analogy is Kaluza-Klein compactification, where local gauge invariance emerges because modes that would resolve the internal coordinate have been integrated out above the compactification scale. The strong coupling boundary condition alpha_s⁻¹(y_s) = 4π follows from the wall-sector contact action, giving y_s = y_wall ≈ 3.65 TeV when run to M_Z with standard QCD. The fractional departure from logarithmic running grows as (µ/y_s)², reaching approximately 0.2% at 1 TeV, 1% at 2 TeV, and 9% at the scaffold scale. The Lorentzian form y_s²/(µ² + y_s²) is distinguishable from a step-function threshold by its smooth rollover and is in principle observable at a 100 TeV collider. The strong coupling boundary condition depends on the wall-sector contact-fibre lemma, which remains unproven and is the outstanding open problem of the programme.

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