{"paper":{"title":"Higher (gauged) Wess--Zumino--Witten terms based on Lie crossed modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Danhua Song","submitted_at":"2026-04-12T02:20:01Z","abstract_excerpt":"We derive higher Wess--Zumino--Witten (WZW) and gauged WZW (gWZW) terms within strict higher Chern--Simons (CS) gauge theory. Starting from the Cartan homotopy formula, we obtain the $(2n+2)$-dimensional higher CS forms and transgression forms for strict Lie 2-groups presented by Lie crossed modules. Given two 2-connections related by a higher gauge transformation, higher transgression forms yield canonical higher WZW and gWZW terms. We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derivation assumes that strict Lie 2-groups are presented by Lie crossed modules and that a symmetric invariant polynomial exists for the associated differential crossed modules, allowing the Cartan homotopy formula to produce the required transgression forms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Higher WZW terms vanish and gauged versions are exact for symmetric invariant polynomials on differential crossed modules, making higher CS actions gauge-invariant on closed manifolds with boundary dependence isolated.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0be5eadcd9deb39691483a4c49bc6f5ebfebf595c5a682655ee6664a947d3066"},"source":{"id":"2604.10416","kind":"arxiv","version":2},"verdict":{"id":"2dddd567-1d4b-4cbf-b740-9d71d21a804c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T16:29:45.924742Z","strongest_claim":"We prove that, for the symmetric invariant polynomial associated with differential crossed modules, the pure-gauge higher WZW term vanishes identically, whereas the higher gWZW term is exact. Consequently, the higher CS action is higher-gauge invariant on closed manifolds, and on manifolds with boundary all gauge dependence is encoded in boundary terms.","one_line_summary":"Higher WZW terms vanish and gauged versions are exact for symmetric invariant polynomials on differential crossed modules, making higher CS actions gauge-invariant on closed manifolds with boundary dependence isolated.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derivation assumes that strict Lie 2-groups are presented by Lie crossed modules and that a symmetric invariant polynomial exists for the associated differential crossed modules, allowing the Cartan homotopy formula to produce the required transgression forms.","pith_extraction_headline":"For differential crossed modules the pure-gauge higher WZW term vanishes identically while the gauged term is exact."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10416/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"}