{"paper":{"title":"$\\mathrm{G}_2$-structures with torsion and the deformed Shatashvili-Vafa vertex algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.DG","authors_text":"Andoni De Arriba de La Hera, Mario Garcia-Fernandez, Mateo Galdeano","submitted_at":"2025-02-04T23:23:23Z","abstract_excerpt":"We construct representations of the deformed Shatashvili-Vafa vertex algebra $\\mathrm{SV}_a$, with parameter $a \\in \\mathbb{C}$, as recently proposed in the physics literature by Fiset and Gaberdiel. The geometric input for our construction are integrable $\\mathrm{G}_2$-structures with closed torsion, solving the heterotic $\\mathrm{G}_2$ system with $\\alpha'=0$ on the group manifolds $S^3\\times T^4$ and $S^3\\times S^3\\times S^1$. From considerations in string theory, one expects the chiral algebra of these backgrounds to include $\\mathrm{SV}_a$, and we provide a mathematical realization of thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02769","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/2502.02769/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"}