{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4d485e1c61513115622c580ca74c33bae8d8afe8eacdb7f6b82e627b8150ca11","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b3a67223872475d133fe0732e08aacf4538d1cfa5c1a3d0c49fc309223b2fe46","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"qft.generalized-symmetries.gaplessness","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Some symmetries force a theory to have massless particles or a degenerate vacuum. A test telling which non-invertible symmetries do this exists only in two dimensions.","posed_since":"","precise":"For a QFT with a finite non-invertible symmetry $C$, find a computable criterion on $C$ that decides whether a trivially gapped, symmetric, non-degenerate phase is possible. In 2D the criterion is the existence of a fiber functor for the fusion category $C$; find the analogue in $d=3 \\text{ and } 4$.","problem_ref":null,"references":"","settled_by":"A theorem stating the criterion for $d = 3, 4$ with examples where it forces gaplessness or degeneracy.","status_note":"Settled in $2\\mathrm{D}$ (2018-2023); open in $d \\ge 3$.","title":"When do non-invertible symmetries forbid a featureless gapped phase","topic_ref":"5eb0476a75858c5dd523d1082965cb71e335c77a7a5cf121927138b7c11c6ef2"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"268ac9c627bff0d07ce2720b7aaa2b61e453d4beaca7286161ce4787093b748a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b7a868b86d5325d7ea60233ba078483b706ba09dfdf4fc327cd3a663831c286b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YC-MB-qos_UtZTzRu00KJsXsdl0b7hErFGtDnKoqJXNeUpa2RBlOyZBP9Ct6bKeUn4ln2WjtMgXHXT7zxRE4Ag"},"schema":"pubphys.envelope/1"},"record_hash":"268ac9c627bff0d07ce2720b7aaa2b61e453d4beaca7286161ce4787093b748a","leaf_index":1910}