Non-Abelian fields in AdS$_4$ spacetime: axially symmetric, composite configurations

Abstract

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers $(m, n)$, where $m$ is related to the polar angle and $n$ to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of Yang-Mills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck--Yang-Mills equations. The variation of the gravitational coupling constant $\alpha$ reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of $\alpha$. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime. Also, a spherically symmetric, closed form solution is found as a perturbation around the globally anti-de Sitter vacuum state.Comment: 30 pages, 15 figure