What question did this study set out to answer?

The aim is to demonstrate a flat-but-holonomic anomaly invariant within the presentation/scheme-bundle framework.

January 26, 2026Open Access

Paper 6: Holonomy Without Curvature - A Flagship Demonstration in the Presentation-Scheme-Bundle Framework

Key Points

The aim is to demonstrate a flat-but-holonomic anomaly invariant within the presentation/scheme-bundle framework.
Constructed a loop of admissible background data for analysis.
Computed the pulled-back local anomaly curvature.
Proved invariance of the nontrivial U(1) phase under admissible local counterterms.
Provided explicit computations for a quantized torsion 2-group example.
Included a continuous large-gauge holographic example.
The local anomaly curvature was shown to vanish despite the nontrivial U(1) phase.
The nontrivial phase was proven invariant across admissible local counterterms.
Explicit computations validated the flagship example involving root-of-unity holonomy.
A continuous AdS5 example exhibited the same mechanisms.

Abstract

We provide a definitive, checkable demonstration of a “flat-but-holonomic” anomaly invariantin the presentation/scheme-bundle framework: along an explicitly constructed loop of admissiblebackground data, the pulled-back local anomaly curvature vanishes, yet the amplitude lineacquires a nontrivial U(1) phase. We prove this phase is invariant under the full class ofadmissible local counterterms. The main text gives a quantized torsion 2-group flagship example(root-of-unity holonomy) with a fully explicit computation; a concise Appendix provides acontinuous large-gauge holographic example (AdS5) exhibiting the same mechanism.

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