{"paper":{"title":"Vortex Harmonic Spinors on the Nappi-Witten Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Vortex configurations on Riemann surfaces lift to harmonic spinors on the Nappi-Witten space and induce Abelian magnetic zero-modes on Minkowski spacetime.","cross_cats":["math.DG"],"primary_cat":"hep-th","authors_text":"Calum Ross, Ra\\'ul S\\'anchez Gal\\'an","submitted_at":"2026-04-07T10:25:41Z","abstract_excerpt":"We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi--Witten space, the group manifold of a central extension of the Euclidean group $SE(2)$. Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation. Using the conformal flatness of the Nappi--Witten metric, these solutions induce harmonic spinors on four-dimensional Minkowski space. This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The conformal flatness of the Nappi-Witten metric allows the lifted solutions to induce harmonic spinors on four-dimensional Minkowski space.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Vortex data on flat surfaces induces explicit harmonic spinors on Minkowski space through solutions on the Nappi-Witten geometry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Vortex configurations on Riemann surfaces lift to harmonic spinors on the Nappi-Witten space and induce Abelian magnetic zero-modes on Minkowski spacetime.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5084b57bc75946f30054c448145688276a2b87fdc97a7cf3492c08f932acfa96"},"source":{"id":"2604.05676","kind":"arxiv","version":2},"verdict":{"id":"ecba919f-6f1d-4217-840a-134f5d87400e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T19:43:31.490344Z","strongest_claim":"This yields a geometric construction of Abelian magnetic zero-modes on flat Minkowski spacetime from vortex data.","one_line_summary":"Vortex data on flat surfaces induces explicit harmonic spinors on Minkowski space through solutions on the Nappi-Witten geometry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The conformal flatness of the Nappi-Witten metric allows the lifted solutions to induce harmonic spinors on four-dimensional Minkowski space.","pith_extraction_headline":"Vortex configurations on Riemann surfaces lift to harmonic spinors on the Nappi-Witten space and induce Abelian magnetic zero-modes on Minkowski spacetime."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.05676/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"cdc670f34c1b997d913639a4344d861b1dfa9cd800e8f86a9d0848e279fd0ed1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}