{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6282e94e048449f81a45936716e9878fdcb2ec2728166eb6b7253177816b3f8e","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4816ed45bd68e0bb8200637d29ae3ef98e7af023c50891aad5c9dd3c990a66bb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"qft.confinement.theta-pi-su2","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Gluon theories have a hidden angle, $\\theta$; at $\\theta = \\pi$ a consistency argument forbids a simple featureless vacuum. For two colors it is unknown whether the vacuum splits into two mirror-image copies or does something else.","posed_since":"2017","precise":"In $4\\mathrm{D}$ $\\mathrm{SU}(N)$ Yang-Mills with topological angle $\\theta$, the mixed anomaly between the $Z_N$ one-form center symmetry and CP at $\\theta = \\pi$ (Gaiotto, Kapustin, Komargodski, Seiberg 2017) forbids a trivially gapped confining vacuum. For $N = 2$, determine whether the vacuum at $\\theta = \\pi$ breaks CP spontaneously (two degenerate vacua and a first-order jump of the topological charge density), is deconfined (including gapped with topological order), or is gapless. Large-N arguments favor CP breaking.","problem_ref":null,"references":"","settled_by":"A sign-problem-free computation (tensor network, quantum simulation, or controlled continuation from imaginary $\\theta$) showing whether the topological charge density jumps at $\\theta = \\pi$ in the continuum limit.","status_note":"Anomaly matching (2017) restricts the options; numerical studies near $\\theta = \\pi$ remained inconclusive as of 2025.","title":"Vacuum structure of $\\mathrm{SU}(2)$ Yang-Mills theory at $\\theta = \\pi$","topic_ref":"76d9445640fcdddaf873735659f32eec87522b700e01144540417b9ab8366050"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"34d5d8eafeecc396500679bbc4cb3fffaabea1ec3681f0ed05c1b0c373592520","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b54c494e351b8f26ef18b35ea9b5590bad04a26d0cf058ac96d6c58ad68180f6","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"zZCe7yQVB-Gl8Tb9zveB0HMn8PTq1UYo9a4OeMtf6t1iBJwt6RKMraf9VCERDYlCa2eZtGkE70qOtsPBYhHGCA"},"schema":"pubphys.envelope/1"},"record_hash":"34d5d8eafeecc396500679bbc4cb3fffaabea1ec3681f0ed05c1b0c373592520","leaf_index":1902}