{"paper":{"title":"3+1d Boundaries with Gravitational Anomaly of 4+1d Invertible Topological Order for Branch-Independent Bosonic Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat","hep-ph","hep-th","math.AT"],"primary_cat":"cond-mat.str-el","authors_text":"Juven Wang, Xiao-Gang Wen, Zheyan Wan","submitted_at":"2021-12-22T18:59:31Z","abstract_excerpt":"We study bosonic systems on a spacetime lattice defined by path integrals of commuting fields. We introduce branch-independent bosonic (BIB) systems, whose path integral is independent of the branch structure of the spacetime simplicial complex, even for a spacetime with boundaries. In contrast, a generic lattice bosonic (GLB) system's path integral may depend on the branch structure. We find the invertible topological order characterized by the Stiefel-Whitney cocycle (e.g., 4+1d w$_2$w$_3$) to be nontrivial for BIB systems, but this topological order and a trivial gapped tensor product state"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.12148","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/2112.12148/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"}