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We find a surprising coincidence, which gives a powerful hint about the nature of the corresponding duality wall.\n  Concretely, we determine the branching rules for the small $N=4$ superconformal algebra at central charge $-9$ as well as for the generic large $N=4$ superconformal algebra at central charge $-6$. Moreover we obtain "},"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":"1804.09821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-04-25T22:30:22Z","cross_cats_sorted":["hep-th","math.RT"],"title_canon_sha256":"76ca9516aba3121052146a9ce97fc16c529760a188af2963ee6a8f8fcd640113","abstract_canon_sha256":"600e919bf352775f741df8bdf3cc436f32987e3b5aa0d2a8eb701bce15832f30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:01:59.928128Z","signature_b64":"SXYUxnu6cpRnZBbrzGEz7fwqwhgH+iXlDy+v6M1w0BatPIybfFDDScEsPK2QV1UeKdDe+mfComQwp+bJJ9WWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24c8e422ac6db26172a0c2ce6f6c413a6e541efb3b4cbc27c1d95c9cab1a73d9","last_reissued_at":"2026-07-05T01:01:59.927773Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:01:59.927773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"S-duality for the large $N=4$ superconformal algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.RT"],"primary_cat":"math.QA","authors_text":"Andrew R. Linshaw, Davide Gaiotto, Thomas Creutzig","submitted_at":"2018-04-25T22:30:22Z","abstract_excerpt":"We prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program. In particular, we present the conjectural kernel vertex algebra for the $S T^2 S$ duality transformation in $SU(2)$ gauge theory. We find a surprising coincidence, which gives a powerful hint about the nature of the corresponding duality wall.\n  Concretely, we determine the branching rules for the small $N=4$ superconformal algebra at central charge $-9$ as well as for the generic large $N=4$ superconformal algebra at central charge $-6$. 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