Pinched Multi Affine Geometry and Confinement: Describing the Yang-Mills Mass Gap
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916657819025408 |
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| author | Gauvin, Shoshauna |
| author_facet | Gauvin, Shoshauna |
| contents | We introduce a multi affine geometric framework in which spacetime curvature relaxes non-instantaneously, subject to a fundamental Planck-scale limit on volumetric contraction. This pinched geometry is shown to localize high-energy distributions, leading to effective constraints on curvature that manifest as a discrete energy gap. Our analysis explores how this limiting curvature dispersion rate not only yields an intuitive explanation of the Yang-Mills mass gap by enforcing a finite tension between non-Abelian color sources. In parallel, we connect these results to an information-geometric viewpoint, demonstrating how the Fisher-Rao curvature quantifies localization pinning in both classical and quantum settings. The resulting picture suggests that quantized excitations and confinement emerge naturally once one accounts for a maximum relaxation speed of curved manifolds. We conclude by outlining how these ideas could be tested through lattice gauge theory comparisons and by examining low-energy glueball spectra, shedding light on a potential geometric unification of gravitational and quantum phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pinched Multi Affine Geometry and Confinement: Describing the Yang-Mills Mass Gap Gauvin, Shoshauna General Physics We introduce a multi affine geometric framework in which spacetime curvature relaxes non-instantaneously, subject to a fundamental Planck-scale limit on volumetric contraction. This pinched geometry is shown to localize high-energy distributions, leading to effective constraints on curvature that manifest as a discrete energy gap. Our analysis explores how this limiting curvature dispersion rate not only yields an intuitive explanation of the Yang-Mills mass gap by enforcing a finite tension between non-Abelian color sources. In parallel, we connect these results to an information-geometric viewpoint, demonstrating how the Fisher-Rao curvature quantifies localization pinning in both classical and quantum settings. The resulting picture suggests that quantized excitations and confinement emerge naturally once one accounts for a maximum relaxation speed of curved manifolds. We conclude by outlining how these ideas could be tested through lattice gauge theory comparisons and by examining low-energy glueball spectra, shedding light on a potential geometric unification of gravitational and quantum phenomena. |
| title | Pinched Multi Affine Geometry and Confinement: Describing the Yang-Mills Mass Gap |
| topic | General Physics |
| url | https://arxiv.org/abs/2503.15539 |