{"paper":{"title":"Classical Symmetry TFTs for Continuous Symmetries via Higher Symplectic Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.MP","math.QA","math.SG"],"primary_cat":"math-ph","authors_text":"Hao Xu","submitted_at":"2026-06-02T09:15:25Z","abstract_excerpt":"We propose a shifted-symplectic formulation of a classical continuous analogue of the symmetry TFT paradigm. Let $G$ be an algebraic or Lie group acting by topological defects on an $n$-dimensional classical topological sigma model with target an $(n-1)$-shifted symplectic derived stack $(X,\\omega)$ via the AKSZ construction. We argue that the corresponding $(n+1)$-dimensional bulk theory should be the AKSZ theory with target the shifted cotangent stack $T^*[n] (\\mathrm B G)$, equivalently the $(n+1)$-dimensional BF theory for $G$. We characterize the Dirichlet and Neumann boundary conditions,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03368","kind":"arxiv","version":1},"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/2606.03368/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"}