Strong Unification without Group Embedding: A Spectral-Action Approach with Graded Superconnection and ℓ-Scaling
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2025
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| _version_ | 1866902050525151232 |
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| author | Hwang, Seokhyun |
| author_facet | Hwang, Seokhyun |
| contents | <p>This work develops a spectral-action based approach to strong unification that does not rely on embedding the Standard Model and gravity into a simple Lie group. Instead, all bosonic sectors are packaged into a graded superconnection that includes the spin connection, gauge fields, the Higgs multiplet, and a scaled tetrad. With this construction, the curvature of the superconnection yields, under a single Clifford–internal trace, the Einstein–Hilbert term linearly together with the Yang–Mills and Higgs kinetic sectors. Dimensional consistency is maintained through the explicit introduction of a length scale, and the entire bosonic action is governed by one unified coupling. In this way the framework realizes single field, single symmetry, and single coupling unification of gravity and the Standard Model. At the unification scale the couplings coincide structurally, while standard renormalization group running explains the observed splitting at low energies. The appendix provides trace prescriptions and positivity arguments to ensure the absence of ghosts and to guarantee unitarity. This formulation establishes a consistent and embedding-free route to strong unification within the spectral-action paradigm, offering a new perspective on the convergence of geometry and particle physics.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16950366 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Strong Unification without Group Embedding: A Spectral-Action Approach with Graded Superconnection and ℓ-Scaling Hwang, Seokhyun <p>This work develops a spectral-action based approach to strong unification that does not rely on embedding the Standard Model and gravity into a simple Lie group. Instead, all bosonic sectors are packaged into a graded superconnection that includes the spin connection, gauge fields, the Higgs multiplet, and a scaled tetrad. With this construction, the curvature of the superconnection yields, under a single Clifford–internal trace, the Einstein–Hilbert term linearly together with the Yang–Mills and Higgs kinetic sectors. Dimensional consistency is maintained through the explicit introduction of a length scale, and the entire bosonic action is governed by one unified coupling. In this way the framework realizes single field, single symmetry, and single coupling unification of gravity and the Standard Model. At the unification scale the couplings coincide structurally, while standard renormalization group running explains the observed splitting at low energies. The appendix provides trace prescriptions and positivity arguments to ensure the absence of ghosts and to guarantee unitarity. This formulation establishes a consistent and embedding-free route to strong unification within the spectral-action paradigm, offering a new perspective on the convergence of geometry and particle physics.</p> |
| title | Strong Unification without Group Embedding: A Spectral-Action Approach with Graded Superconnection and ℓ-Scaling |
| url | https://doi.org/10.5281/zenodo.16950366 |