{"paper":{"title":"Topological non-linear $\\sigma$-model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Chenchang Zhu, Tian Lan, Xiao-Gang Wen","submitted_at":"2018-08-28T16:30:24Z","abstract_excerpt":"A discrete non-linear $\\sigma$-model is obtained by triangulate both the space-time $M^{d+1}$ and the target space $K$. If the path integral is given by the sum of all the complex homomorphisms $\\phi: M^{d+1} \\to K$, with an partition function that is independent of space-time triangulation, then the corresponding non-linear $\\sigma$-model will be called topological non-linear $\\sigma$-model which is exactly soluble. Those exactly soluble models suggest that phase transitions induced by fluctuations with no topological defects (i.e. fluctuations described by homomorphisms $\\phi$) usually produ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09394","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":""},"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"}