Dyons and dyonic black holes in suðNÞ Einstein-Yang-Mills theory in anti–de Sitter spacetime

We present new spherically symmetric, dyonic soliton and black hole solutions of the suðNÞ EinsteinYang-Mills equations in four-dimensional asymptotically anti–de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N − 1 magnetic gauge field functions and N − 1 electric gauge field functions. We explore the phase space of solutions in detail for suð2Þ and suð3Þ gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.