Non-Abelian vacua in D=5, N=4 gauged supergravity

We study essentially non-Abelian backgrounds in the five dimensional N=4 gauged SU(2) x U(1) supergravity. Static configurations that are invariant under either the SO(4) spatial rotations or with respect to the SO(3) rotations and translations along the fourth spatial coordinate are considered. By analyzing consistency conditions for the equations for supersymmetric Killing spinors we derive the Bogomol'nyi equations and obtain their globally regular solutions. The SO(4) symmetric configurations contain the purely magnetic non-Abelian fields together with the purely electric Abelian field and possess two unbroken supersymmetries. The SO(3) configurations have only the non-Abelian fields and preserve four supersymmetries. (author)