Which gluon field configurations cause quark confinement
In plain words
Computer simulations show that quarks are confined, but they do not say which shapes of the gluon field are responsible. Candidate answers include thin tubes of field (vortices) and magnetic monopoles, point-like sources of magnetic field.
Precise statement
In $4\mathrm{D}$ $\mathrm{SU}(N)$ Yang-Mills theory, identify the class of gauge-field configurations (center vortices, Abelian monopoles in a chosen gauge, calorons and their dyon constituents, or other) whose statistics reproduce the area law $\langle W(C)\rangle \sim \exp(-\sigma A)$ of large Wilson loops, the full string tension $\sigma$, Casimir scaling of string tensions at intermediate distances and N-ality dependence at large distances. An answer is a gauge-invariant (or demonstrably gauge-independent) definition of the configurations, together with evidence that removing them removes $\sigma$ and keeping only them reproduces it.
What would settle it
A gauge-invariant identification of the configurations, checked by continuum-extrapolated lattice Monte Carlo, that accounts for the full string tension and its dependence on the quark representation.
Status in the literature
Unverified note
Center-vortex and monopole pictures each reproduce much of the string tension in lattice studies, but both rely on gauge fixing and neither is accepted as complete (2025).
Related problems
- More general than Does small-circle semiclassical confinement connect smoothly to four dimensions
- More general than Do center vortices alone give the full SU(3) string tension
See also
- Related Vacuum structure of $\mathrm{SU}(2)$ Yang-Mills theory at $\theta = \pi$
- Related Worldsheet theory of the confining flux tube at large N
- Related Sharp distinction between Higgs and confining phases with fundamental matter
- Related Does confinement imply chiral symmetry breaking in QCD-like theories
- Related Ratio of k-string tensions in large-N Yang-Mills theory