U(1) Gauge Field of the Kaluza-Klein Theory in the Presence of Branes

TL;DR

This paper explores how the presence of a brane affects the U(1) gauge symmetry in Kaluza-Klein theories, revealing that while the effective action breaks gauge invariance, linearized analysis shows the symmetry persists at the perturbative level.

Contribution

It demonstrates that the U(1) gauge symmetry is explicitly broken in the effective action but remains intact at the linearized level in the presence of a brane without orbifold symmetry.

Findings

Effective 4D action lacks gauge invariance due to brane effects.

Linearized perturbations preserve U(1) gauge symmetry.

The graviscalar exhibits different behavior from standard models.

Abstract

We investigate the zero mode dimensional reduction of the Kaluza-Klein unifications in the presence of a single brane in the infinite extra dimension. We treat the brane as fixed, not a dynamical object, and do not require the orbifold symmetry. It seems that, contrary to the standard Kaluza-Klein models, the 4D effective action is no longer invariant under the U(1) gauge transformations due to the explicit breaking of isometries in the extra dimension by the brane. Surprisingly, however, the linearized perturbation analysis around the RS vacuum shows that the Kaluza-Klein gauge field does possess the U(1) gauge symmetry at the linear level. In addition, the graviscalar also behaves differently from the 4D point of view. Some physical implications of our results are also discussed.