Consilience Note: Harmonic Excitation Modes in QCD Flux-Tube Confinement

Quantum chromodynamics (QCD) describes quark confinement through gluonic flux tubes connecting quark–antiquark pairs. Lattice QCD simulations have shown that these confinement structures support discrete excitation spectra corresponding to quantized energy levels above the ground-state flux tube. These excitations are commonly interpreted using effective string models in which the flux tube behaves as a vibrating relativistic string. However, independent of the specific modeling framework, the simulations empirically demonstrate that the confinement geometry supports structured excitation modes. This note highlights the compatibility of these observations with harmonic structural interpretations in which admissible excitation modes arise from the geometry of the confinement container. Under such interpretations, particle states correspond to stable excitations of constrained standing modes within the gluonic flux-tube structure.