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

TL;DR

This paper studies scalar fields saturating the Breitenlohner-Freedman bound in asymptotically Anti-de Sitter spacetimes, revealing a slower metric fall-off and modified asymptotic symmetries due to a logarithmic branch in the scalar field.

Contribution

It introduces new asymptotic conditions and symmetry analysis for scalar fields with logarithmic branches in AdS spacetimes, extending previous understanding of boundary behaviors.

Findings

Scalar field exhibits a logarithmic branch decreasing as r^{-(D-1)/2} ln r.

Asymptotic symmetry generators remain finite with the scalar field's logarithmic behavior.

Modified asymptotic conditions preserve the conformal symmetry group in D-1 dimensions.

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.