On models of gauge field localization on a brane
S. L. Dubovsky, V. A. Rubakov
TL;DR
The paper investigates two gauge-field localization schemes on a flat brane: a bulk-confinement (Shifman–Dvali) mechanism and a brane-induced localization term. It shows that confinement in the bulk with a vanishing confinement scale on the brane yields a massless localized photon, a $D$-dimensional Coulomb law on the brane, and charge universality enforced by confining strings; conversely, brane-induced localization works poorly for $d>1$, since the field inside the brane is not truly four-dimensional and the bulk gauge coupling becomes strong, compromising non-Abelian viability. In the special case of a single extra dimension ($d=1$), charge universality holds automatically, but the bulk remains strongly coupled if the effective four-dimensional coupling is order one, posing a tension between localization and perturbativity. The work highlights that graviton-like localization on a brane faces similar dimensionality-dependent challenges and reinforces that realistic localization must preserve the equivalence principle and four-dimensional gauge interactions across scales.
Abstract
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 4-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.