Non-minimal couplings in Randall-Sundrum Scenarios

TL;DR

This paper introduces a novel method to generate four-dimensional gauge fields from a five-dimensional bulk in Randall-Sundrum models using only non-minimal gravitational couplings, avoiding additional fields.

Contribution

It demonstrates that two specific non-minimal couplings can produce massless gauge fields on the brane without extra degrees of freedom, with parameters fixed by boundary conditions.

Findings

Achieves gauge invariance without extra fields

Provides analytical solutions for zero modes

Requires fine tuning of coupling parameters

Abstract

In this paper we propose a new way of obtaining four dimensional gauge invariant $U(n)$ gauge field from a bulk action. The results are valid for both Randall-Sundrum scenarios and are obtained without the introduction of other fields or new degrees of freedom. The model is based only in non-minimal couplings with the gravity field. We show that two non-minimal couplings are necessary, one with the field strength and the other with a mass term. Despite the loosing of five dimensional gauge invariance by the mass term a massless gauge field is obtained over the brane. To obtain this, we need of a fine tuning of the two parameters introduced through the couplings. The fine tuning is obtained by imposing the boundary conditions and to guarantee non-abelian gauge invariance in four dimensions. With this we are left with no free parameters and the model is completely determined. The model also provides analytical solutions to the linearized equations for the zero mode and for a general warp factor.