Features of gravity-Yang-Mills hierarchies in d-dimensions

TL;DR

This paper explores higher-dimensional Einstein-Yang-Mills systems with p-form curvature terms, constructing solutions in various dimensions that generalize known lower-dimensional solutions and identifying exact solutions in specific cases.

Contribution

It introduces higher-dimensional gravity-Yang-Mills hierarchies, constructs finite-energy solutions, and generalizes classical solutions like Bartnik-McKinnon and BTZ to higher dimensions.

Findings

Finite mass-energy solutions in dimensions 2p+2 to 4p.

Complete analogy with d=4p Einstein-Yang-Mills systems.

Exact solutions found in the case d=2p+1.

Abstract

Higher dimensional, direct analogues of the usual d=4 Einstein--Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d=4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in $2p+2\le d \le 4p$, in which dimensions the total mass-energy is finite, generalising the familiar Bartnik-McKinnon solutions in EYM theory for p=1. In d=4p, this similarity is complete. In the special case of d=2p+1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d=2p+1 purely gravitational systems, whose solutions generalise the static d=3 BTZ solutions, are discussed.