Dyonic black holes in $\mathfrak{s}\mathfrak{u}(\mathrm{\infty })$ anti-de Sitter Einstein-Yang-Mills theory, characterised by an infinite set of global charges

We here investigate static, spherically symmetric solutions to $\mathfrak{s}\mathfrak{u}(\mathrm{\infty })$ Einstein-Yang-Mills theory with a negative cosmological constant $\mathrm{\Lambda }$ in the case of dyonic solutions, which possess a non-trivial electric sector of the gauge field. We are able to find non-trivial solutions to this system, and show that some may be uniquely characterised by a countably infinite set of global charges, which may have implications for Bizon’s modified `No Hair’ theorem.