Gauge field localization on Abelian vortices in six dimensions

TL;DR

This paper investigates how gauge fields and metric fluctuations behave in six-dimensional Abelian Higgs vortex models, showing that gauge fields can be localized while graviphotons cannot, with implications for gravity localization.

Contribution

It provides a detailed analysis of vector and tensor fluctuations in 6D Abelian Higgs vortices, revealing the localization properties of gauge and graviphoton zero modes.

Findings

Tensor zero modes are normalizable and decoupled.

Gauge field zero modes are localized and normalizable.

Graviphoton zero modes are not localized.

Abstract

The vector and tensor fluctuations of vortices localizing gravity in the context of the six-dimensional Abelian Higgs model are studied. These string-like solutions break spontaneously six-dimensional Poincar\'e invariance leading to a finite four-dimensional Planck mass and to a regular geometry both in the bulk and on the core of the vortex. While the tensor modes of the metric are decoupled and exhibit a normalizable zero mode, the vector fluctuations, present in the gauge sector of the theory, are naturally coupled to the graviphoton fields associated with the vector perturbations of the warped geometry. Using the invariance under infinitesimal diffeomorphisms, it is found that the zero modes of the graviphoton fields are never localized. On the contrary,the fluctuations of the Abelian gauge field itself admit a normalizable zero mode.