Localization of Matter and Cosmological Constant on a Brane in Anti de Sitter Space

TL;DR

This paper investigates how matter fields and the cosmological constant can be localized on a brane within five-dimensional anti de Sitter space, proposing a model that allows for a zero four-dimensional cosmological constant through a four-form gauge field.

Contribution

It introduces a mechanism using a four-form gauge field to achieve a continuous family of brane solutions with adjustable cosmological constant, including a zero value.

Findings

Spin-zero fields are localized on positive-tension branes.

A continuous tower of states exists without a mass gap.

A four-form gauge field enables tuning of the cosmological constant.

Abstract

We study two issues, the localization of various spin fields, and the problem of the cosmological constant on a brane in five-dimensional anti de Sitter space. We find that spin-zero fields are localized on a positive-tension brane. In addition to the localized zero-mode there is a continuous tower of states with no mass gap. Spin one-half and three-half states can be localized on a brane with ``negative tension''. Their localization can be achieved on the positive-tension brane as well, if additional interactions are introduced. The necessary ingredient of the scenario with localized gravity is the relation between the bulk cosmological constant and the brane tension. In the absence of supersymmetry this implies fine-tuning between the parameters of the theory. To deal with this issue we introduce a four-form gauge field. This gives an additional arbitrary contribution to the bulk cosmological constant. As a result, the model gives rise to a continuous family of brane Universe solutions for generic values of the bulk cosmological constant and the brane tension. Among these solutions there is one with a zero four-dimensional cosmological constant.