  We consider both the Abelian Higgs model and the impact of a minimal length
in the un-particle sector. It is shown that even if the Higgs field takes a
non-vanishing v.e.v., gauge interaction keeps its long range character leading
to an effective gauge symmetry restoration. The effect of a quantum gravity
induced minimal length on a physical observable is then estimated by using a
physically-based alternative to the usual Wilson loop approach. Interestingly,
we obtain an ultraviolet finite interaction energy described by a confluent
hyper-geometric function, which shows a remarkable richness of behavior.
