On models of gauge field localization on a brane

We argue that any viable mechanism of gauge field localization should automatically imply charge universality on the brane. We study whether this condition is satisfied in the two known proposals aimed to localize vector field in flat bulk space. We construct a simple calculable model with confinement in the bulk and deconfinement on the brane, as in the Shifman-Dvali set-up. We find that in our model the four-dimensional Coulomb law is indeed reproduced on the brane due to the massless localized photon mode. The charge universality is enforced by the presence of "confining strings." On the other hand, charge universality condition is not satisfied in another, brane-induced localization mechanism when the number of extra dimensions d is larger than two. We demonstrate that in the non-Abelian case the gauge fields inside the brane are never four-dimensional and their self-interaction is strong at all distances of interest. Hence this mechanism does not work for d > 2. At d = 2 the charge universality is still a problem, but it holds automatically at d = 1. At d = 1, however, the bulk gauge fields are strongly coupled in the non-Abelian case.