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

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.