Localized non-Abelian gauge fields in non-compact extra-dimensions

TL;DR

This paper presents a method for localizing non-Abelian gauge fields in non-compact extra dimensions using a field-dependent kinetic term, ensuring four-dimensional gauge invariance and analyzing various models.

Contribution

It introduces a universal framework for dynamical localization of non-Abelian gauge fields in non-compact dimensions and extends gauge fixing methods for clear mode separation.

Findings

Massless four-dimensional gauge modes are localized on solitons.

The approach maintains unbroken four-dimensional gauge invariance.

Models in 5, 6, and 7 dimensions demonstrate the method's applicability.

Abstract

Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typically arises in the presence of topological solitons. We construct four-dimensional low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the $R_\xi$ gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the four-dimensional components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken four-dimensional gauge invariance. We illustrate our methods with models in $D=5$ (domain walls), in $D=6$ (vortices), and in $D=7$.