A Formalism to Analyze the Spectrum of Brane World Scenarios

TL;DR

This paper introduces a formalism for analyzing perturbations in complex gravitational and field systems, especially in warped geometries relevant to brane world models, including localization of gauge fields.

Contribution

It develops a general bilinear action framework for small fluctuations around arbitrary solutions in higher-dimensional theories, applied to gauge field localization in brane scenarios.

Findings

Nielsen-Olesen string yields localized spin-1 field in any dimension

Formalism separates fluctuations into decoupled spin sectors

Application to gauge localization in warped geometries

Abstract

In this paper we develop a formalism to analyze the spectrum of small perturbations about arbitrary solutions of Einstein, Yang-Mills and scalar systems. We consider a general system of gravitational, gauge and scalar fields in a $D-$dimensional space-time and give the bilinear action for the fluctuations of the fields in the system around an arbitrary solution of the classical field equations. We then consider warped geometries, popular in brane world scenarios, and use the light cone gauge to separate the bilinear action into a totally decoupled spin-two, -one and -zero fluctuations. We apply our general scheme to several examples and discuss in particular localization of abelian and non-abelian gauge fields of the standard model to branes generated by scalar fields. We show in particular that the Nielsen-Olsen string solution gives rise to a normalizable localized spin-1 field in any number of dimensions.