{"paper":{"title":"Free-Field Construction of Heterotic String Compactified on Calabi-Yau Orbifolds via Correspondence with $\\mathcal{N}{=}2$ SCFT Minimal Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Alexander Belavin, Doron Gepner, Grigory Makarov","submitted_at":"2026-06-25T19:14:06Z","abstract_excerpt":"We establish a correspondence between the free-field construction and the minimal-model construction of the Calabi--Yau sector of the four-dimensional heterotic string compactified on Berglund--H\\\"{u}bsch type Calabi--Yau manifolds and their orbifolds. For Fermat-type polynomials the Calabi--Yau vertex operators expressed in terms of free fields are shown to correspond to products of primary fields of $\\mathcal{N}{=}2$ minimal models. Using this correspondence we verify modular invariance of the free-field construction and extend it to Berglund--H\\\"{u}bsch Calabi--Yau orbifolds, deriving the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27490","kind":"arxiv","version":1},"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/2606.27490/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"}