Wilson lines, de Rham theorem, and proton spin decomposition controversy

The geometric approach based on parallel transport and Wilson lines to gain insight into the decomposition of the gluon gauge 4-vector potential is being developed in the literature to address the proton spin puzzle. Unfortunately, conflicting claims on the uniqueness of the decomposition have been made. We reexamine this controversy and argue that Hodge decomposition and the de Rham theorem resolve this issue in a natural way such that the topological defects acquire a fundamental significance. It is suggested that qualitatively angular momentum holonomy could be an alternative new mechanism to account for the deficit proton spin.