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Lifting Klein-Gordon/Einstein solutions to general nonlinear sigma-models: the wormhole example

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Brax, Philippe 
Quevedo, F 


jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an jats:italicarbitrary</jats:italic> solution to the coupled Einstein/Klein-Gordon field equations for a single scalar field jats:italicσ</jats:italic> to a solution of the nonlinear sigma-model for jats:italicN</jats:italic> scalar fields minimally coupled to gravity. This mapping between solutions does not require there to be any target-space isometries and exists for every choice of geodesic computed using the target-space metric. In some special situations — such as when the solution depends only on a single coordinate (e.g. for homogeneous time-dependent or static spherically symmetric configurations) — the general solution to the sigma-model equations can be obtained in this way. We illustrate the technique by applying it to generate Euclidean wormhole solutions for multi-field sigma models coupled to gravity starting from the simplest Giddings-Strominger wormhole, clarifying why in the wormhole case Minkowski-signature target-space geometries can arise. We reproduce in this way the well-known axio-dilaton string wormhole and we illustrate the power of the technique by generating simple perturbations to it, like those due to string or jats:italicα</jats:italic>′ corrections.</jats:p>


Acknowledgements: We thank Adam Solomon for helpful conversations. CB’s research was partially supported by funds from the Natural Sciences and Engineering Research Council (NSERC) of Canada. Research at the Perimeter Institute is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. The work of FQ has been partially supported by STFC consolidated grants ST/P000681/1, ST/T000694/1.


4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

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Journal of High Energy Physics

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Springer Science and Business Media LLC