On models of gauge field localization on a brane

TL;DR

This paper examines gauge field localization mechanisms on branes, showing that charge universality is achieved in some models with confinement but not in others, especially for higher dimensions.

Contribution

It compares different localization proposals, demonstrating that charge universality depends on the number of extra dimensions and the nature of the bulk confinement.

Findings

Charge universality holds in models with confinement and d=1.

Charge universality fails for d>2 in brane-induced mechanisms.

Non-Abelian gauge fields are strongly coupled inside the brane for d>1.

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.