{"paper":{"title":"Surface defects, flavored modular differential equations and modularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Haocong Zheng, Yiwen Pan, Yufan Wang","submitted_at":"2022-07-21T13:05:16Z","abstract_excerpt":"Every 4d $\\mathcal{N} = 2$ SCFT $\\mathcal{T}$ corresponds to an associated VOA $\\mathbb{V}(\\mathcal{T})$, which is in general non-rational with a more involved representation theory. Null states in $\\mathbb{V}(\\mathcal{T})$ can give rise to non-trivial flavored modular differential equations, which must be satisfied by the refined/flavored character of all the $\\mathbb{V}(\\mathcal{T})$-modules. Taking some $A_1$ theories $\\mathcal{T}_{g,n}$ of class-$\\mathcal{S}$ as examples, we construct the flavored modular differential equations satisfied by the Schur index. We show that three types of surf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.10463","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/2207.10463/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"}