{"paper":{"title":"Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A three-dimensional quantum field theory can carry an infinite-dimensional symmetry given by a centrally extended affine graded Lie algebra.","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Hank Chen, Joaquin Liniado","submitted_at":"2025-07-02T16:17:39Z","abstract_excerpt":"We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra. Accordingly, this setup provides a framework for ex"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a centrally extended affine graded Lie algebra can be realized as the symmetry algebra of a consistent, anomaly-free three-dimensional quantum field theory.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A 3D QFT is defined with infinite-dimensional topological-holomorphic symmetry from a centrally extended affine graded Lie algebra, yielding a raviolo vertex algebra for its local operators after radial quantization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A three-dimensional quantum field theory can carry an infinite-dimensional symmetry given by a centrally extended affine graded Lie algebra.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5782dfac2df3d369d7a4817fa6cb8eb72067618f506d581010e584f309dce706"},"source":{"id":"2507.01858","kind":"arxiv","version":4},"verdict":{"id":"b66e8747-b628-4fae-9258-b40b69596cdd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T06:13:16.572426Z","strongest_claim":"Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analogue of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra.","one_line_summary":"A 3D QFT is defined with infinite-dimensional topological-holomorphic symmetry from a centrally extended affine graded Lie algebra, yielding a raviolo vertex algebra for its local operators after radial quantization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a centrally extended affine graded Lie algebra can be realized as the symmetry algebra of a consistent, anomaly-free three-dimensional quantum field theory.","pith_extraction_headline":"A three-dimensional quantum field theory can carry an infinite-dimensional symmetry given by a centrally extended affine graded Lie algebra."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.01858/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":44,"sample":[{"doi":"10.1016/0550-3213(84)90052-x","year":1984,"title":"Infi- nite Conformal Symmetry in Two-Dimensional Quantum Field Theory","work_id":"55beb8e5-94f6-45ce-b42d-22a06e61239f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Lectures on the Infrared Structure of Gravity and Gauge Theory","work_id":"3ba280da-c35c-4327-b5c2-c4efaf7d073c","ref_index":3,"cited_arxiv_id":"1703.05448","is_internal_anchor":true},{"doi":"","year":2021,"title":"Celestial Holog- raphy","work_id":"4e591fc9-54b8-42e3-b356-d1462665ddce","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/jhep10(2022)193","year":2022,"title":"Celestial holography meets twisted holography: 4d amplitudes from chiral correlators","work_id":"ad365e10-1aa6-4e5c-9667-3478d503c253","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physrevlett.129.231604","year":2022,"title":"Associativity of One-Loop Cor- rections to the Celestial Operator Product Expansion","work_id":"60f5ce5c-f578-431e-94e4-a6d338cfd0f5","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":44,"snapshot_sha256":"98e6c23e58884fd6df5339e4606b12c5c2a8b6237b100464c7088244f80a068d","internal_anchors":7},"formal_canon":{"evidence_count":2,"snapshot_sha256":"46cd0bd9ba8a97c913834083e60ab56cd1a5e4dd8e01849fac492fccd7bd7846"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}