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

Abstract

We here investigate static, spherically symmetric solutions to $\mathfrak{su}(\infty )$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$ 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.

38 pages, 4 figures

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