{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"03c0e6a6139885fd424e699bcee2d47ca1141a42d02ce6338cfb74a626f1e85a","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1915c230c5fb95538d6f72bdea80b2f3f423c806ffafcdab22c2e39444e70946","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qft.confinement.chiral-from-confinement","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"In QCD, quark confinement comes with the spontaneous breaking of chiral symmetry (the symmetry rotating left- and right-handed quarks separately), which makes pions nearly massless. Whether confinement always forces this breaking, for any number of colors and quark types, is not proven.","posed_since":"1980","precise":"In 4D $\\mathrm{SU}(N_{c})$ gauge theory with $N_{f}$ massless Dirac quarks in the fundamental representation, assume confinement in the sense that all massless bound states are color singlets. Prove that $\\mathrm{SU}(N_{f})_{L}$ x $\\mathrm{SU}(N_{f})_{R}$ breaks to $\\mathrm{SU}(N_{f})_{V}$ for every $N_{c} \\ge 3$ and every $N_{f}$ below the conformal window, using 't Hooft anomaly matching without further dynamical assumptions, or exhibit a consistent chirally symmetric confining spectrum.","problem_ref":null,"references":"","settled_by":"A proof from anomaly matching and the confinement assumption alone covering every $N_{c} \\ge 3$ and every $N_{f}$ below the conformal window, or a consistent massless-baryon spectrum that matches all anomalies.","status_note":"Ciambriello, Contino, Luzio, Romano and Xu (2024, arXiv:2404.02967) proved breaking for $N_{f} \\ge p_{\\mathrm{min}}$, the smallest prime factor of $N_{c}$; smaller $N_{f}$ requires assuming no phase transition as quark masses are sent to infinity.","title":"Does confinement imply chiral symmetry breaking in QCD-like 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