{"paper":{"title":"Tunnels Under Geometries (or Instantons Know Their Algebras)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Alexei Morozov, Dmitry Galakhov","submitted_at":"2025-02-16T22:34:09Z","abstract_excerpt":"In the tight binding model with multiple degenerate vacua we might treat wave function overlaps as instanton tunnelings between different wells (vacua). An amplitude for such a tunneling process might be constructed as $\\mathsf{T}_{i\\to j}\\sim e^{-S_{\\mathrm{ inst}}}{\\mathbf{v}}_j^{+}{\\mathbf{v}}_i^{-}$, where there is canonical instanton action suppression, and $\\mathbf{v}_i^{-}$ annihilates a particle in the $i^{\\mathrm{th}}$ vacuum, whereas $\\mathbf{v}_j^{+}$ creates a particle in the $j^{\\mathrm{th}}$ vacuum. Adiabatic change of the wells leads to a Berry-phase evolution of the couplings, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.11294","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.11294/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}