{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a24d35f2711f0334fffa2cded6545f372923a301d43af1662dade8435673ee86","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ab4c83677022ff8d8ac7381403ba1c0dd6667b2569bc21cce80c5bbfb2a26ed4","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"9d978a41d43e29b8e5917ab67461027bdbcd5dd26b6eb820879bbad71ec6e278","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":"2","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":"ab4c83677022ff8d8ac7381403ba1c0dd6667b2569bc21cce80c5bbfb2a26ed4","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 $N_{f} \\ge p_{\\min}$, 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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