Ultraviolet Matching Across Coherence Boundaries in Projector-Defined Gauge Theories: Spectral Persistence, Response Transport, and an Application to the Axis Model
Andrew Morton · Public preprint · Conditional matching and persistence
Defines the evidence needed to match a projector-based gauge theory across changes in its internal sector or spacetime description.
Abstract
Effective theories whose gauge fields arise from smoothly selected internal subspaces require a matching prescription when those subspaces, or the spacetime geometry used to define them, become unavailable at higher energies. We distinguish the breakdown of an approximation from the loss of a protected spectral projector or a nondegenerate coframe, identifying separate scales for approximation control, gauge-sector definability, metric definability, coherent reconstruction, and microscopic matching. An explicit constant-gap example shows that order-one projector deformation does not establish disappearance of the selected sector. When ultraviolet evolution mixes that sector with its complement, matching requires transport of the full microscopic response, or an independently justified equivalent invariant, before reconstruction and projection. Spectral selection, collective response, and curvature-source coupling have distinct mathematical roles. Within the local source-induced normalization class, an independently normalized equivariant source gives g_H⁻² = λ_H; relating this coefficient to a projected response weight requires additional microscopic factorization, and independent bare or threshold contributions must be included separately. Applying these results to the Axis Model, a proposed coherence-based microscopic construction, separates its estimated coherence-control scale from its proposed ultraviolet matching scale without assuming that the required low-energy structures persist between them. The microscopic origin of the weak-sector projector, its source normalization, and the persistence-or-transition mechanism remain undetermined. The Axis application therefore defines a conditional ultraviolet-to-EFT matching architecture rather than a completed ultraviolet theory.
Scope
The results distinguish approximation control, spectral persistence, geometric definability and microscopic matching. A physical continuation requires normalized sources and controlled persistence or transition. Physical boundary scales and an ultraviolet completion remain to be selected.
Paper and supporting files
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