{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d937f4b7dc1695d1be25c0ab932036bf6b2f0ad116d31fda2a6194123bd80138","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["268ac9c627bff0d07ce2720b7aaa2b61e453d4beaca7286161ce4787093b748a","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"79ee0f90af86e85c20821d3b2a602b2166b8cd8ccd641c07b1fa135a43a51c7b","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":"2","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":"268ac9c627bff0d07ce2720b7aaa2b61e453d4beaca7286161ce4787093b748a","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"3d0ea00e8b5395e05656f406da175cbdead45e6e73fd0eac34297c24a8957f2a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"296441a1547843c574ff518928afb41f442c4e113e0c946a60a22c9d02784d0a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sekIg-WnZCGY7fxa9-vGskf9QAy4T96bZdgNLSUX4zMBhKew_TFVCvd9YpHttk0sdpB42w13xbVj5s_2dP_wAw"},"schema":"pubphys.envelope/1"},"record_hash":"3d0ea00e8b5395e05656f406da175cbdead45e6e73fd0eac34297c24a8957f2a","leaf_index":3646}