{"paper":{"title":"Rationality of Lorentzian Lattice CFTs And The Associated Modular Tensor Category","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Madhav Sinha, Ranveer Kumar Singh, Runkai Tao","submitted_at":"2024-08-05T18:01:53Z","abstract_excerpt":"We classify the irreducible modules of a rational Lorentzian lattice vertex operator algebra (LLVOA) based on an even, self-dual Lorentzian lattice $\\Lambda\\subset\\mathbb{R}^{m,n}$ of signature $(m,n)$. We show that the set of isomorphism classes of irreducible modules of the LLVOA are in one-to-one correspondence with the equivalence classes $\\Lambda_0^\\circ/\\Lambda_0$ for a certain subset $\\Lambda_0^\\circ\\subset\\mathbb{R}^{m,n}$ and a full rank sublattice $\\Lambda_0\\subset\\Lambda$. We also classify the intertwining operators between the modules and calculate the fusion rules. We then describ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02744","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/2408.02744/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"}