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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_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.4808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-06-18T17:31:38Z","cross_cats_sorted":[],"title_canon_sha256":"914f5413a50a04f175240378b3fadc762967f7ad7ddaee4d2a9550656d7ac110","abstract_canon_sha256":"392cd46159dca992c21926bed65426637de63cdc4886b9d6ce7dba6b8a7cba3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:30.256429Z","signature_b64":"JxNBDsZ/a020n79a4ybdY/0K71rolKP4LsPUxB6OOzUvNLWoHyYM7t1a2TVz3iLVKD/p/aHcaR+QUNCV0G61Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcc817fa4c106ca89e4d9946a58715f11b978db084c7b8318ef1922f11d85261","last_reissued_at":"2026-05-18T02:49:30.255961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:30.255961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $D(2,1;\\alpha)$. 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