Non-Abelian Bogomol'nyi-Prasad-Sommerfield Monopoles in $\mathit{N}=4\mathrm{}$ Gauged Supergravity

We study static, spherically symmetric, and purely magnetic solutions of $\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)$ gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory.