{"paper":{"title":"Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Eduardo Fradkin, Meng Cheng, Peng Ye","submitted_at":"2017-01-19T19:00:03Z","abstract_excerpt":"In this paper, we propose a generalization of the $S$-duality of four-dimensional quantum electrodynamics ($\\text{QED}_4$) to $\\text{QED}_4$ with fractionally charged excitations, the fractional $S$-duality. Such $\\text{QED}_4$ can be obtained by gauging the $\\text{U(1)}$ symmetry of a topologically ordered state with fractional charges. When time-reversal symmetry is imposed, the axion angle ($\\theta$) can take a nontrivial but still time-reversal invariant value $\\pi/t^2$ ($t\\in\\mathbb{Z}$). Here, $1/t$ specifies the minimal electric charge carried by bulk excitations. Such states with time-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05559","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":""},"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"}