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arXiv · 1409.1894

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

Olga Kichakova·Jutta Kunz·Eugen Radu·Yasha Shnir
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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 $α$ reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of $α$. 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.

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Olga Kichakova, Jutta Kunz, Eugen Radu, Yasha Shnir. 2014-09-05. Non-Abelian fields in AdS$_4$ spacetime: axially symmetric, composite configurations. https://doi.org/10.1103/physrevd.90.124012

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