On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

TL;DR

This paper proves the global existence of topological dyonic black hole and soliton solutions in four-dimensional anti-de Sitter Einstein-Yang-Mills theories with general semisimple gauge groups, extending previous results to more general settings.

Contribution

It establishes the existence of non-trivial, topologically symmetric dyonic solutions for a broad class of gauge groups, including solutions with gauge fields having no zeroes, in anti-de Sitter space.

Findings

Proven existence of solutions near known embedded solutions.

Established solutions as the cosmological constant magnitude increases.

Identified solutions with gauge fields having no zeroes, relevant for stability.

Abstract

Here we study the global existence of `hairy' dyonic black hole and dyon solutions to four dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply-connected and semisimple gauge group $G$, for so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for $\mathfrak{su}(N)$. We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as $|\Lambda|\rightarrow\infty$. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the $\mathfrak{su}(N)$ case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.