# Globally regular solutions to dyonic anti-de Sitter $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory -- Existence and characterising charges

## TL;DR

This paper constructs and characterizes new static, spherically symmetric dyonic solutions in $ ext{su}( ext{infinity})$ Einstein-Yang-Mills theory with a large negative cosmological constant, highlighting their unique charges and mass properties.

## Contribution

It provides the first explicit solutions in this regime and proves their unique characterization by an infinite set of charges and their distinction from black holes by mass.

## Key findings

- Existence of new globally regular dyonic solutions in $ ext{su}( ext{infinity})$ EYM with large negative $ ext{Λ}$.
- Solutions are characterized by a countably infinite set of effective global charges.
- Dyon solutions are distinguished from black hole solutions by their ADM masses.

## Abstract

In this work, we find new static, spherically symmetric, dyonic, globally regular exact solutions to $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory with a negative cosmological constant $\Lambda$, in the regime that $|\Lambda|$ is very large. In this regime, we also prove that dyonic globally regular solutions may be uniquely characterised by a countably infinite set of effective global charges; and that dyon solutions may be distinguished from dyonic black hole solutions to the same field equations by their ADM masses. These solutions have potential modelling applications for certain exotic gravitational objects.