Kaluza-Klein Reduction in a Warp Geometry Revisited

TL;DR

This paper revisits Kaluza-Klein reduction in the Randall-Sundrum model, revealing the existence of zero-modes dependent on the extra dimension and their localization properties on a brane.

Contribution

It demonstrates the presence of non-traditional zero-modes in non-compact extra dimensions and analyzes their localization on the brane.

Findings

Zero-modes depend on the fifth dimension in non-compact reductions.

2-form and 3-form fields on the brane originate from bulk 3-form and 4-form fields.

Zero-mode localization properties are characterized in the Randall-Sundrum setup.

Abstract

We study the Kaluza-Klein dimensional reduction of zero-modes of bulk antisymmetric tensor fields on a non-compact extra dimension in the Randall-Sundrum model. It is shown that in the Kaluza-Klein reduction on a non-compact extra dimension we have in general a zero-mode depending on a fifth dimension in addition to a conventional constant zero-mode in the Kaluza-Klein reduction on a circle. We examine the localization property of these zero-modes on a flat Minkowski 3-brane. In particular, it is shown that a 2-form and a 3-form on the brane can be respectively obtained from a 3-form and 4-form in the bulk by taking the zero-mode dependent on the fifth dimension.