{"paper":{"title":"The Shatashvili-Vafa $G_{2}$ superconformal algebra as a Quantum Hamiltonian Reduction of $D(2,1;\\alpha)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"L\\'azaro O. Rodr\\'iguez D\\'iaz, Reimundo Heluani","submitted_at":"2014-06-18T17:31:38Z","abstract_excerpt":"We obtain the superconformal algebra associated to a sigma model with target a manifold with $G_{2}$ holonomy, i.e., the Shatashvili-Vafa $G_{2}$ algebra as a quantum Hamiltonian reduction of the exceptional Lie superalgebra $D(2,1;\\alpha)$ for $\\alpha=1$. We produce the complete family of $W$-algebras $SW(\\frac{3}{2},\\frac{3}{2}, 2)$ (extensions of the $N=1$ superconformal algebra by two primary supercurrents of conformal weight $\\frac{3}{2}$ and $2$ respectively) as a quantum Hamiltonian reduction of $D(2,1;\\alpha)$. As a corollary we find a free field realization of the Shatashvili-Vafa $G_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4808","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":""},"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"}