{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"850271e8e12cce4277e346a0925a99f432283175a25002db54026f908cc1267e","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["34d5d8eafeecc396500679bbc4cb3fffaabea1ec3681f0ed05c1b0c373592520","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"bc86dd0e7426cbe2f04307dab9f9f8304824b07e4486899443419ddc89c20eb9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":["ai:gpt-5.5"],"external_id":"qft.confinement.theta-pi-su2","kind":"well-posed","literature_status":"open","n":"2","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":"34d5d8eafeecc396500679bbc4cb3fffaabea1ec3681f0ed05c1b0c373592520","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 = 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