No hair conjecture, nonabelian hierarchies and anti-de Sitter spacetime

TL;DR

This paper explores solutions to Einstein-Yang-Mills systems with negative cosmological constant in higher dimensions, addressing mass divergence issues and introducing higher-order Yang-Mills corrections inspired by string theory to obtain finite mass solutions.

Contribution

It introduces higher Yang-Mills hierarchy corrections to achieve finite mass solutions in higher-dimensional AdS spacetimes, extending previous four-dimensional results.

Findings

Mass diverges for dimensions greater than four without corrections.

Higher-order Yang-Mills terms yield finite mass solutions in higher dimensions.

Differences between higher-dimensional and four-dimensional solutions are analyzed.

Abstract

We consider globally regular and black holes solutions for the Einstein-Yang-Mills system with negative cosmological constant in $d-$spacetime dimensions. We find that the ADM mass of the spherically symmetric solutions generically diverges for $d>4$. Solutions with finite mass are found by considering corrections to the YM Lagrangean consisting in higher therm of the Yang--Mills hierarchy. Such systems can occur in the low energy effective action of string theory. A discussion of the main properties of the solutions and the differences with respect to the four dimensional case is presented. The mass of these configurations is computed by using a counterterm method.