Spheres, Deficit Angles and the Cosmological Constant

TL;DR

This paper investigates how different bulk field configurations in higher-dimensional gravity theories affect the stability of the four-dimensional cosmological constant when branes with tension are introduced, highlighting the advantages of four-form fields over monopoles.

Contribution

It demonstrates that using a four-form field in higher-dimensional compactifications avoids fine-tuning issues related to brane tension and extends solutions to arbitrary dimensions.

Findings

Monopole configurations reintroduce fine-tuning due to gauge field quantization.

Four-form fields allow arbitrary brane tension without affecting the 4D cosmological constant.

The solutions are generalized to higher dimensions with arbitrary brane tension.

Abstract

We consider compactifications of six dimensional gravity in four dimensional Minkowski or de Sitter space times a two dimensional sphere, S^2. As has been recently pointed out, it is possible to introduce 3-branes in these backgrounds with arbitrary tension without affecting the effective four dimensional cosmological constant, since its only effect is to induce a deficit angle in the sphere. We show that if a monopole like configuration of a 6D U(1) gauge field is used to produce the spontaneous compactification of the two extra dimensions in a sphere a fine tuning between brane and bulk parameters is reintroduced once the quantization condition for the gauge field is taken into account, so the 4D cosmological constant depends on the brane tension. This problem is absent if instead of the monopole we consider a four form field strength in the bulk to obtain the required energy-momentum tensor. Also, making use of the four form field, we generalize the solution to an arbitrary number of dimensions (\ge 6), keeping always four noncompact dimensions and compactifying the rest in a n-dimensional sphere. We show that a (n+1)-brane with arbitrary tension can be introduced in this background without affecting the effective 4D cosmological constant.