Toward a Unified Picture of Confinement and Baryon Structure

Abstract

In this work, we investigate the infrared structure of quantum chromodynamics from the perspective of the Cho-Faddeev-Niemi decomposition and the Faddeev-Niemi effective theory of Yang-Mills fields. We argue that the topological solitons of the Faddeev-Niemi theory, namely gluon knots characterized by the Hopf invariant, should be regarded as the relevant ground-state degrees of freedom of Yang-Mills theory in the deep infrared region. In this framework, gluon knots provide a unified description of monopole condensation and the center-vortex confinement mechanism. We further propose that baryons are composite objects consisting of quarks immersed in a gluon-knot background. The monopole condensate associated with the gluon knot realizes dual superconductivity, squeezes color-electric flux into flux tubes, and naturally generates the $\mathrm{Y}$-shaped confinement structure of baryons. Simultaneously, the strong local color-magnetic field generated by the gluon knot induces chiral symmetry breaking through magnetic catalysis and topological vacuum fluctuations. We show that the Hopf invariant of the gluon knot is closely related to the topology of Yang-Mills vacua and discuss its connection with the axial anomaly and instanton-induced chiral symmetry breaking. Furthermore, the topological current associated with gluon knots provides a natural carrier of gluon angular momentum and may account for a substantial fraction of the proton spin. The resulting picture establishes a possible connection between the infrared topology of Yang-Mills theory and the internal structure of baryons, providing a unified framework for confinement, chiral symmetry breaking, and baryon structure in QCD.

29 pages, 6 figures