{"paper":{"title":"A geometric free field realisation for the genus-two class $\\mathcal{S}$ theory of type $\\mathfrak{a}_1$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Carlo Meneghelli, Christopher Beem","submitted_at":"2021-04-23T15:51:40Z","abstract_excerpt":"We present a free field realisation for the vertex operator algebra associated to the genus-two, class $\\mathcal{S}$ superconformal field theory of type $\\mathfrak{a}_1$. The free field realisation is in the style of recent work by the authors, and is formulated in terms of a one-dimensional isotropic lattice vertex algebra along with two pairs of symplectic fermions. Our realisation makes manifest an enhanced ${\\rm USp}(4)$ outer automorphism group of the VOA that is inherited from the symplectic fermion system. This extends an ${\\rm SU(2)}$ outer automorphism that has been observed in recent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.11668","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/2104.11668/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"}