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Gauge Dynamics: Charges, Scales, and Phases

Gauge theories describe forces through fields with redundant coordinates. Their physical phases must therefore be distinguished using gauge-invariant quantities: charge and flux sectors, spectra, static energies, and suitable line operators. This chapter connects these diagnostics to screening, dynamically generated scales, and theta dependence.

Enter this chapter

Section titled “Enter this chapter”

Begin with Dynamical Gauge Fields and Matter to connect the gauge action to its physical charges and constraints.

Topics

Section titled “Topics”
  1. Dynamical Gauge Fields and Matter — Introduces dynamical connections, matter, and Gauss constraints.
  2. Charges, Screening, and Long-Range Forces — Relates charge to flux and identifies screening channels.
  3. Coulomb, Higgs, and Confining Regimes — Compares gauge-invariant infrared diagnostics of different regimes.
  4. Gauge-Phase Diagnostics from Line Operators — Tests which line operators can distinguish the specified theory’s phases.
  5. Running and Dynamical Scales in Gauge Theories — Derives a dynamical scale from the running gauge coupling.
  6. Theta Dependence in Yang–Mills and QCD — Connects topological sectors to theta-dependent observables.

How the ideas fit together

Section titled “How the ideas fit together”

The meaning of a line operator depends on the global gauge group and the dynamical matter. Matter capable of screening an external probe can break its flux tube, so a fundamental Wilson-loop area law need not remain an asymptotic confinement criterion. Spectral gaps, screening, and symmetry realization answer related but distinct questions. In particular, a gauge-fixed field expectation value cannot replace a physical phase diagnostic. These distinctions explain why pure Yang–Mills criteria cannot simply be transferred to QCD with light quarks. Gaiotto et al. 2015, § 5.

Where to go next

Section titled “Where to go next”

Continue to Quantum Electrodynamics to identify the fields, charge convention, and observables of the Abelian theory.

References

Section titled “References”
  • Gaiotto, Davide, Anton Kapustin, Nathan Seiberg, and Brian Willett. “Generalized Global Symmetries.” Journal of High Energy Physics 2015, no. 2 (2015): 172, §5, pp. 28–33. DOI. Open PDF.