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Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch

Marc Henneaux·Cristian Martinez·Ricardo Troncoso·Jorge Zanelli
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Abstract

We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D \geq 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D-1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field.

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Marc Henneaux, Cristian Martinez, Ricardo Troncoso, Jorge Zanelli. 2004-07-02. Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch. https://doi.org/10.1103/physrevd.70.044034

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