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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18821829 |
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| _version_ | 1866901944639946752 |
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| author | Kulkarni, Raghu |
| author_facet | Kulkarni, Raghu |
| contents | <p>We present a rigorous resolution to the Nielsen-Ninomiya “No-Go” theorem by deriv-</p> <p>ing fermion chirality from the non-bipartite topology of a saturated cuboctahedral vacuum</p> <p>(K = 12). Standard hypercubic discretizations of the Dirac equation inevitably produce</p> <p>spurious mirror fermions due to the bipartite symmetry of the grid. We demonstrate that a</p> <p>Face-Centered Cubic (FCC) lattice, formed of simplicial tetrahedra, introduces topological</p> <p>frustration that breaks this symmetry. By explicitly constructing the discrete Dirac operator</p> <p>and specifying the Γ<span>j </span>matrices as spin projections along the 12 bond directions, we evaluate</p> <p>the dispersion relation across the first Brillouin zone. We show that while the physical mode</p> <p>at the Γ-point is massless, doubler modes at the L and X points are lifted to the Planck</p> <p>cutoff. To validate this geometric framework, we derive the bare Higgs coupling λ ≈0.125</p> <p>from the ratio of surface-to-volume configurations, predicting a mass of 123.11 GeV.</p> <p>Keywords: Fermion Doubling, Nielsen-Ninomiya Theorem, Lattice Field Theory, Higgs Mass, Grav-</p> <p>itational Echoes, Selection-Stitch Model</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18821829 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Fermion Chirality from Non-Bipartite Topology: Resolving the Doubling Problem via Lattice Saturation Kulkarni, Raghu <p>We present a rigorous resolution to the Nielsen-Ninomiya “No-Go” theorem by deriv-</p> <p>ing fermion chirality from the non-bipartite topology of a saturated cuboctahedral vacuum</p> <p>(K = 12). Standard hypercubic discretizations of the Dirac equation inevitably produce</p> <p>spurious mirror fermions due to the bipartite symmetry of the grid. We demonstrate that a</p> <p>Face-Centered Cubic (FCC) lattice, formed of simplicial tetrahedra, introduces topological</p> <p>frustration that breaks this symmetry. By explicitly constructing the discrete Dirac operator</p> <p>and specifying the Γ<span>j </span>matrices as spin projections along the 12 bond directions, we evaluate</p> <p>the dispersion relation across the first Brillouin zone. We show that while the physical mode</p> <p>at the Γ-point is massless, doubler modes at the L and X points are lifted to the Planck</p> <p>cutoff. To validate this geometric framework, we derive the bare Higgs coupling λ ≈0.125</p> <p>from the ratio of surface-to-volume configurations, predicting a mass of 123.11 GeV.</p> <p>Keywords: Fermion Doubling, Nielsen-Ninomiya Theorem, Lattice Field Theory, Higgs Mass, Grav-</p> <p>itational Echoes, Selection-Stitch Model</p> |
| title | Fermion Chirality from Non-Bipartite Topology: Resolving the Doubling Problem via Lattice Saturation |
| url | https://doi.org/10.5281/zenodo.18821829 |