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

## TL;DR

This paper explores static, spherically symmetric dyonic black hole solutions in $rak{su}( ext{infinity})$ Einstein-Yang-Mills theory with negative cosmological constant, revealing solutions characterized by an infinite set of global charges.

## Contribution

It presents the first known solutions in this theory with a non-trivial electric sector, characterized by an infinite set of global charges, challenging traditional 'No Hair' theorems.

## Key findings

- Existence of non-trivial dyonic solutions in $rak{su}( ext{infinity})$ Einstein-Yang-Mills theory.
- Solutions are characterized by a countably infinite set of global charges.
- Implications for modifications of the 'No Hair' theorem in the context of infinite gauge groups.

## 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.