Localization of Vector Field on Dynamical Domain Wall

TL;DR

This paper explores various mechanisms for localizing vector fields, including gauge fields and gravitons, on a dynamical domain wall embedded in five-dimensional spacetime, with implications for brane-world cosmology.

Contribution

It investigates three formulations for vector field localization on a dynamical domain wall, extending previous work and analyzing the graviton's vector components in an expanding universe.

Findings

Vector fields can be localized via different mechanisms on the domain wall.

The graviton's vector components are localized similarly to gauge fields.

Corrections from the bulk dimension affect localization in an expanding universe.

Abstract

In the previous works (arXiv:1202.5375 and 1402.1346), the dynamical domain wall, where the four dimensional FRW universe is embedded in the five imensional space-time, has been realized by using two scalar fields. In this paper, we consider the localization of vector field in three formulations. The first formulation was investigated in the previous paper (arXiv:1510.01099) for the $U(1)$ gauge field. In the second formulation, we investigate the Dvali-Shifman mechanism (hep-th/9612128), where the non-abelian gauge field is confined in the bulk but the gauge symmetry is spontaneously broken on the domain wall. In the third formulation, we investigate the Kaluza-Klein modes coming from the five dimensional graviton. In the Randall-Sundrum model, the graviton was localized on the brane. We show that the $(5,\mu)$ components $\left(\mu=0,1,2,3\right)$ of the graviton are also localized on the domain wall and can be regarded as the vector field on the domain wall. There are, however, some corrections coming from the bulk extra dimension if the domain wall universe is expanding.