Nontrivial SU(2) Holonomy and Residual Geometric Frustration on the Diamond Lattice in Granular Entropic Physics
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901391855845376 |
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| author | Sekanina, Štěpán |
| author_facet | Sekanina, Štěpán |
| contents | <p>We compute the SU(2) Wilson loop around the minimal hexagonal cycle on the diamond lattice using holonomies prescribed by Granular Entropic Physics (GEP). For pi-rotation holonomies U = i(sigma dot e) along tetrahedral edge directions, the Wilson loop evaluates to Tr(W) = -10/27, corresponding to an effective flux angle of approximately 101 degrees. This is a gauge-invariant, non-Abelian result: the trace uniquely determines the conjugacy class in SU(2), confirming a genuine nontrivial flux sector. Unlike Z2 frustration, which is annihilated by the bipartite structure of the diamond lattice, SU(2) frustration persists due to non-commutativity. The number -10/27 is a geometric invariant determined entirely by the tetrahedral structure, not a tunable parameter. This result establishes a necessary condition for the GEP cosmological constant mechanism: microscopic frustration is not a gauge artifact but a gauge-invariant geometric property of the network.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20060111 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Nontrivial SU(2) Holonomy and Residual Geometric Frustration on the Diamond Lattice in Granular Entropic Physics Sekanina, Štěpán SU(2) holonomy Wilson loop diamond lattice geometric frustration non-Abelian gauge theory tetrahedral simplex granular entropic physics cosmological constant bipartite lattice gauge invariance <p>We compute the SU(2) Wilson loop around the minimal hexagonal cycle on the diamond lattice using holonomies prescribed by Granular Entropic Physics (GEP). For pi-rotation holonomies U = i(sigma dot e) along tetrahedral edge directions, the Wilson loop evaluates to Tr(W) = -10/27, corresponding to an effective flux angle of approximately 101 degrees. This is a gauge-invariant, non-Abelian result: the trace uniquely determines the conjugacy class in SU(2), confirming a genuine nontrivial flux sector. Unlike Z2 frustration, which is annihilated by the bipartite structure of the diamond lattice, SU(2) frustration persists due to non-commutativity. The number -10/27 is a geometric invariant determined entirely by the tetrahedral structure, not a tunable parameter. This result establishes a necessary condition for the GEP cosmological constant mechanism: microscopic frustration is not a gauge artifact but a gauge-invariant geometric property of the network.</p> |
| title | Nontrivial SU(2) Holonomy and Residual Geometric Frustration on the Diamond Lattice in Granular Entropic Physics |
| topic | SU(2) holonomy Wilson loop diamond lattice geometric frustration non-Abelian gauge theory tetrahedral simplex granular entropic physics cosmological constant bipartite lattice gauge invariance |
| url | https://doi.org/10.5281/zenodo.20060111 |