Brane solutions of a spherical sigma model in six dimensions

TL;DR

This paper investigates six-dimensional gravity coupled with a spherical sigma model, analyzing brane solutions that are finite, singularity-free, and explore their potential for self-tuning the cosmological constant.

Contribution

It provides new brane solutions in a spherical sigma model context, addressing scalar field single-valuedness and self-tuning features in six-dimensional models.

Findings

Solutions are finite volume and singularity free under certain conditions.

Scalar fields can be embedded to ensure single-valuedness.

Self-tuning features are present but do not fully explain the cosmological constant problem.

Abstract

We explore solutions of six dimensional gravity coupled to a non-linear sigma model, in the presence of co-dimension two branes. We investigate the compactifications induced by a spherical scalar manifold and analyze the conditions under which they are of finite volume and singularity free. We discuss the issue of single-valuedness of the scalar fields and provide some special embedding of the scalar manifold to the internal space which solves this problem. These brane solutions furnish some self-tuning features, however they do not provide a satisfactory explanation of the vanishing of the effective four dimensional cosmological constant. We discuss the properties of this model in relation with the self-tuning example based on a hyperbolic sigma model.