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Asymptotically anti–de Sitter spacetimes and scalar fields with a logarithmic branch

par Henneaux, Marc ;Martínez, Cristián;Troncoso, Ricardo ;Zanelli, Jorge
Référence Physical review. D, Particles, fields, gravitation, and cosmology, 70, 4, page (4)
Publication Publié, 2004

Article révisé par les pairs

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Résumé :

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 [Formula Presented] 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 [Formula Presented] 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 [Formula Presented] 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. © 2004 The American Physical Society.