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Confinement and Chiral QCD

This chapter has two connected routes through infrared QCD. The confinement route asks what can be defined or diagnosed once dynamical quarks can screen external color; the chiral route derives how the QCD symmetry, anomaly, and vacuum realization determine pion physics. Choose by the output you need, and keep pure Yang–Mills statements separate from claims about QCD with light quarks.

Enter this chapter

Section titled “Enter this chapter”

Begin with What Confinement Means in QCD with Dynamical Quarks to distinguish QCD confinement from an unbreakable flux-tube criterion.

Topics

Section titled “Topics”
  1. What Confinement Means in QCD with Dynamical Quarks — Defines confinement questions in the presence of dynamical quarks.
  2. Static Sources, Center Symmetry, and String Breaking in QCD — Explains how screening changes static-source observables.
  3. QCD Confinement versus the Yang–Mills Mass Gap — Separates confinement diagnostics from a spectral-gap existence theorem.
  4. Chiral Symmetry in QCD — Determines exact and anomalous flavor symmetries.
  5. Chiral Order Parameters, Current Algebra, and Pions — Connects spontaneous chiral breaking to pion current matrix elements.
  6. Chiral Lagrangians and Low-Energy QCD — Organizes low-energy pion interactions in a controlled expansion.
  7. The U(1)A Problem and QCD Topology — Relates the singlet axial anomaly to gauge-field topology.

How the ideas fit together

Section titled “How the ideas fit together”

Confinement and chiral symmetry breaking describe different features of infrared QCD. Screening affects the interpretation of external color probes, while the realization of an approximate global chiral symmetry determines the light pion degrees of freedom. The latter supports a derivative expansion even when quark-and-gluon perturbation theory fails. The anomalous singlet axial symmetry must be treated separately: it does not supply another ordinary Goldstone boson. No single order parameter proves all of these claims. Weinberg 1996, §§ 19.4–19.5 and 19.10.

Where to go next

Section titled “Where to go next”

Continue to Hadrons and Heavy Quarks to classify color-singlet states before selecting a dynamical approximation.

References

Section titled “References”
  • Weinberg, Steven. The Quantum Theory of Fields. Volume II: Modern Applications. Cambridge: Cambridge University Press, 1996. DOI.