Non-Abelian Gauge Structure from Coherence-Gated Internal Symmetries: A Projection Mechanism and a Kernel-to-Coupling Map
Andrew Morton · Published · AIP Advances (2026) · Conditional gauge geometry
A coherent, protected internal sector supports a gauge-covariant non-Abelian connection and curvature construction under stated domain assumptions.
Current program context
The deposited abstract is reproduced unchanged. The Action-Level and UV Matching papers provide the current treatment of coupling normalization, including independent source strengths and the conditions required for complete factorization.
Abstract
We present an effective-theory framework showing that, on a coherent domain Ω_coh where a stable rank-2 internal sector exists as a smooth bundle, the local freedom to choose an orthonormal frame induces an SU(2) gauge structure in the Wilczek–Zee sense. The analysis is explicitly conditional: we do not derive the dynamical origin of the coherence field Φ nor of the rank-2 sector, but characterize the geometric and response-theoretic consequences once a smooth rank-2 projector P_Φ(x) is given on Ω_coh. The induced connection obeys the standard inhomogeneous transformation law, yields the covariant derivative and Yang–Mills curvature on Ω_coh, and admits the projector identity F_μν = −iW†[∂_μP_Φ, ∂_νP_Φ]W (with an explicit nonzero-curvature example). We formalize “coherence gating” as a strict restriction of the domain of definition—a domain-of-validity principle rather than a claim that physical decoherence is sharp—so gauge observables are defined on Ω_coh and are not assumed to extend across ∂Ω_coh, avoiding the gauge-noncovariance that would result from multiplying a connection by a nonconstant coherence weight. Beyond this kinematic structure, we provide a response-theoretic kernel-to-normalization interface in a quadratic two-leg benchmark: Schur-complement elimination of heavy locking modes yields a dimensionless projected response fraction ω_eff (benchmark ω_eff ≃ 0.296), and the matching-scale inverse coupling is fixed by g⁻²(Λ) = ω_eff/τ₀, where τ₀ > 0 is the coherent-domain stiffness defined via auxiliary two-form (first-order) elimination. In isotropic embeddings τ₀ = τ_sus/(κf_T) with f_T = 2/3; more generally f_T is a computable trace ratio determined by the microscopic (possibly anisotropic) response kernel.
Scope
The construction assumes a coherent domain and a smooth, protected two-dimensional internal sector. It establishes the stated connection and curvature identities within that domain.
Paper and supporting files
A companion Jupyter notebook for the gauge-geometry and quadratic-response benchmark is included in the Zenodo deposit.
Read the current paper and supporting files on Zenodo
Read the journal publication in AIP Advances
Related reading
Joint realization of two response inputs
What determines a gauge coupling?
Matching across coherence boundaries
Abstract checked 28 August 2026 · v6 · public release 20 March 2026.