Validity of the minimal-length flux network (Steiner-tree) model for SU(3) flux tubes

Determine to what extent the idealized thin-string, minimal-length network (Steiner-tree) model accurately reproduces the shapes and energies of flux tubes and hubs in pure SU(3) gauge theory across varied source–anti-source geometries and separations.

Background

To model SU(3) triality flux transport, the paper considers an idealized scenario where flux tubes behave as thin strings with energy strictly proportional to length, leading to a modified Steiner-tree minimization problem with treeon and anti-treeon junctions. This model predicts equiangular junctions and specific configuration transitions (e.g., two-meson vs. tetraquark arrangements).

Whether this geometric minimization framework faithfully captures the actual non-perturbative flux distributions in SU(3) lattice gauge theory remains unsettled, especially at large separations where tubes are most clearly defined but numerically challenging.