Spherically symmetric Yang-Mills solutions in a (4+n)- dimensional space-time

TL;DR

This paper explores spherically symmetric solutions in higher-dimensional Einstein-Yang-Mills theories, deriving analytic solutions for specific conditions and numerically constructing finite energy solutions for the case of two extra dimensions.

Contribution

It provides new analytic Einstein-Maxwell-dilaton solutions and numerical finite energy solutions in a (4+n)-dimensional setting with spherical symmetry.

Findings

Analytic solutions exist for n > 1 with specific Higgs field conditions.

Constructed numerically finite energy solutions for n=2.

Derived effective 4D Einstein-Yang-Mills-Higgs-dilaton models.

Abstract

We consider the Einstein-Yang-Mills Lagrangian in a (4+n)-dimensional space-time. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant exist. We construct the analytic solutions which fulfill this conditions for arbitrary n, namely the Einstein-Maxwell-dilaton solutions. We also present generic solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, which possesses n Higgs triplets coupled in a specific way to n independent dilaton fields. These solutions are the abelian Einstein-Maxwell- dilaton solutions and analytic non-abelian solutions, which have diverging Higgs fields. In addition, we construct numerically asymptotically flat and finite energy solutions for n=2.