Observable Hierarchy and Transport Reconstruction of a Frustrated SU(2) Vacuum on the Diamond Lattice
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901782584623104 |
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| author | Sekanina, Štěpán |
| author_facet | Sekanina, Štěpán |
| contents | <p>We study the 9-dimensional gauge-field fluctuation space above the frustrated SU(2) vacuum (Tr(W) = -10/27) on the diamond lattice within the Granular Entropic Physics programme. A hierarchy of gauge-invariant observables is established, ordered by collective depth. Single traces Tr(W_I) have identically vanishing gradients at the vacuum, a structural SU(2) property. Hexagonal plaquette products (17 invariants including pairwise, triple, quadruple, and commutator structures) saturate at rank 5. Transported observables Tr(W_A T W_B T-dagger) achieve rank 6 per transport topology, consistently across all 30 tested topologies. Full rank-9 reconstruction requires combining at least 3 distinct transport topologies (minimal basis: 9 observables). The reconstruction is highly anisotropic, with effective observable dimension D_eff between 3 and 6, far below the algebraic rank 9. No single transport topology stabilises the Wilson saddle point. The paper includes a self-correction of an earlier dark-sector interpretation, which was shown to be an artifact of an insufficiently rich observable basis rather than a structural property of the vacuum. The central result is that the frustrated vacuum is a transport-sensitive collective phase whose full characterisation requires a multi-topology observable atlas.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20219606 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Observable Hierarchy and Transport Reconstruction of a Frustrated SU(2) Vacuum on the Diamond Lattice Sekanina, Štěpán SU(2) lattice gauge theory frustrated vacuum diamond lattice Wilson loop hierarchy observable reconstruction transport holonomy rank saturation anisotropic observable geometry saddle point stability Hessian analysis tetrahedral symmetry non-Abelian frustration Granular Entropic Physics High Energy Physics - Lattice Mathematical Physics General Relativity and Quantum Cosmology <p>We study the 9-dimensional gauge-field fluctuation space above the frustrated SU(2) vacuum (Tr(W) = -10/27) on the diamond lattice within the Granular Entropic Physics programme. A hierarchy of gauge-invariant observables is established, ordered by collective depth. Single traces Tr(W_I) have identically vanishing gradients at the vacuum, a structural SU(2) property. Hexagonal plaquette products (17 invariants including pairwise, triple, quadruple, and commutator structures) saturate at rank 5. Transported observables Tr(W_A T W_B T-dagger) achieve rank 6 per transport topology, consistently across all 30 tested topologies. Full rank-9 reconstruction requires combining at least 3 distinct transport topologies (minimal basis: 9 observables). The reconstruction is highly anisotropic, with effective observable dimension D_eff between 3 and 6, far below the algebraic rank 9. No single transport topology stabilises the Wilson saddle point. The paper includes a self-correction of an earlier dark-sector interpretation, which was shown to be an artifact of an insufficiently rich observable basis rather than a structural property of the vacuum. The central result is that the frustrated vacuum is a transport-sensitive collective phase whose full characterisation requires a multi-topology observable atlas.</p> |
| title | Observable Hierarchy and Transport Reconstruction of a Frustrated SU(2) Vacuum on the Diamond Lattice |
| topic | SU(2) lattice gauge theory frustrated vacuum diamond lattice Wilson loop hierarchy observable reconstruction transport holonomy rank saturation anisotropic observable geometry saddle point stability Hessian analysis tetrahedral symmetry non-Abelian frustration Granular Entropic Physics High Energy Physics - Lattice Mathematical Physics General Relativity and Quantum Cosmology |
| url | https://doi.org/10.5281/zenodo.20219606 |