Gravitating Yang--Mills fields in all dimensions

TL;DR

This paper classifies gravitating Yang--Mills systems across all dimensions, focusing on finite energy solutions, including regular and black hole types, with emphasis on higher order curvature terms in Einstein and Yang--Mills systems.

Contribution

It provides a comprehensive classification of gravitating Yang--Mills systems in all dimensions, highlighting the role of higher order curvature terms and solution types.

Findings

Finite energy solutions exist in classified systems.

Regular solutions are limits of black holes with vanishing horizon.

Higher order curvature terms are essential in certain systems.

Abstract

A classification of gravitating Yang--Mills systems in all dimensions is presented. These systems are set up so that they support finite energy solutions. Both regular and black hole solutions are considered, the former being the limit of the latter for vanishing event horizon radius. Special attention is paid to systems necessarily involving higher order Yang--Mills curvature terms, along with the option of incorporating higher order terms in the Riemann curvature. The scope here is restricted to Einstein systems, with or without cosmological constant, and the Yang--Mills(--Higgs) systems.