{"paper":{"title":"Boundary-bulk relation in topological orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"cond-mat.str-el","authors_text":"Hao Zheng, Liang Kong, Xiao-Gang Wen","submitted_at":"2017-02-02T13:35:46Z","abstract_excerpt":"In this paper, we study the relation between an anomaly-free $n+$1D topological order, which are often called $n+$1D topological order in physics literature, and its $n$D gapped boundary phases. We argue that the $n+$1D bulk anomaly-free topological order for a given $n$D gapped boundary phase is unique. This uniqueness defines the notion of the \"bulk\" for a given gapped boundary phase. In this paper, we show that the $n+$1D \"bulk\" phase is given by the \"center\" of the $n$D boundary phase. In other words, the geometric notion of the \"bulk\" corresponds precisely to the algebraic notion of the \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00673","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}