Classify all orbit-to-orbit minimizers

Classify all orbit-to-orbit global minimizers for the two distinguished SU(5)×Z₂ matrix field regimes by systematically analyzing all equality cases in the orbit-distance polynomial estimates.

Background

The paper proves that the explicit non-Abelian kinks are global minimizers among all finite-energy connections joining the corresponding vacuum orbits, and that their SU(5) conjugates and translates are also minimizers. However, the continuous vacuum-orbit geometry and the equality conditions in the distance--coarea argument leave open whether additional minimizers exist beyond these symmetry-generated profiles. A complete answer requires analyzing every equality case in the model-specific orbit-distance polynomial comparisons used to establish the sharp lower bounds.