Charged isotropic non-Abelian dyonic black branes

TL;DR

This paper constructs isotropic charged non-Abelian black branes in Einstein-Yang-Mills theory with negative cosmological constant, exploring their properties and differences in even and odd spacetime dimensions, especially regarding magnetic fields and mass divergence.

Contribution

It introduces new isotropic non-Abelian black brane solutions in AdS space, analyzing their properties and the impact of Chern-Simons terms in odd dimensions.

Findings

Solutions are similar to Einstein-Maxwell dyonic branes in even dimensions.

Magnetic field causes divergence in mass in even dimensions.

Chern-Simons terms enable finite-mass solutions with vanishing magnetic fields in odd dimensions.

Abstract

We construct black holes with a Ricci flat horizon in Einstein--Yang-Mills theory with a negative cosmological constant, which approach asymptotically an AdS$_d$ spacetime background (with $d\geq 4$). These solutions are isotropic, $i.e.$ all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein-Maxwell theory (which, however, exist in even spacetime dimensions only). These black branes possess a nonzero magnetic field strength on the flat boundary metric, which leads to a divergent mass of these solutions, as defined in the usual way. However, a different picture is found for odd spacetime dimensions, where a non-Abelian Chern-Simons term can be incorporated in the action. This allows for black brane solutions with a magnetic field which vanishes asymptotically.