{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LJAXAIND5GYX7CIYOLPCLVOUOZ","short_pith_number":"pith:LJAXAIND","schema_version":"1.0","canonical_sha256":"5a417021a3e9b17f891872de25d5d4766ab2ad3162e261b5b0ebb7207ea4d7fc","source":{"kind":"arxiv","id":"1707.07717","version":1},"attestation_state":"computed","paper":{"title":"Constraints on Higher Spin CFT$_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alexander Maloney, Eric Perlmutter, Kale Colville, Nima Afkhami-Jeddi, Thomas Hartman","submitted_at":"2017-07-24T19:36:01Z","abstract_excerpt":"We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with $\\mathcal{W}_N$ symmetry in the \"irrational\" regime, where $c>N-1$ and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when $c>N-1$. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large $c$, this implies that the"},"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":"1707.07717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-07-24T19:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"04e7ebc5f8280f32b789fa29c9d2899922d97ecc59da406dc4ffd27a35cf92b6","abstract_canon_sha256":"26b1d3ed7a7111feb93e4ed7818fb9a49196ca54e229818e099415291fd56ef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:32.274491Z","signature_b64":"X/djFiSa658DJzuUxCwXU9VhJ8bGnUNLeMsqp/7ZS5SzSSau+lmk6FBSwWS/Mj1dQXKJewyjIMg+RePnRN7qBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a417021a3e9b17f891872de25d5d4766ab2ad3162e261b5b0ebb7207ea4d7fc","last_reissued_at":"2026-05-18T00:13:32.273881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:32.273881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constraints on Higher Spin CFT$_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alexander Maloney, Eric Perlmutter, Kale Colville, Nima Afkhami-Jeddi, Thomas Hartman","submitted_at":"2017-07-24T19:36:01Z","abstract_excerpt":"We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with $\\mathcal{W}_N$ symmetry in the \"irrational\" regime, where $c>N-1$ and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when $c>N-1$. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large $c$, this implies that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07717","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.07717","created_at":"2026-05-18T00:13:32.273964+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07717v1","created_at":"2026-05-18T00:13:32.273964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07717","created_at":"2026-05-18T00:13:32.273964+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJAXAIND5GYX","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJAXAIND5GYX7CIY","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJAXAIND","created_at":"2026-05-18T12:31:28.150371+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ","json":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ.json","graph_json":"https://pith.science/api/pith-number/LJAXAIND5GYX7CIYOLPCLVOUOZ/graph.json","events_json":"https://pith.science/api/pith-number/LJAXAIND5GYX7CIYOLPCLVOUOZ/events.json","paper":"https://pith.science/paper/LJAXAIND"},"agent_actions":{"view_html":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ","download_json":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ.json","view_paper":"https://pith.science/paper/LJAXAIND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07717&json=true","fetch_graph":"https://pith.science/api/pith-number/LJAXAIND5GYX7CIYOLPCLVOUOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LJAXAIND5GYX7CIYOLPCLVOUOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ/action/storage_attestation","attest_author":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ/action/author_attestation","sign_citation":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ/action/citation_signature","submit_replication":"https://pith.science/pith/LJAXAIND5GYX7CIYOLPCLVOUOZ/action/replication_record"}},"created_at":"2026-05-18T00:13:32.273964+00:00","updated_at":"2026-05-18T00:13:32.273964+00:00"}