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

By M. Henneaux, Cristián Martínez, Ricardo Troncoso, J. Zanelli. 2004

154 citations recorded by the source corpus.

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 $Dg~3$ 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 ${r}^{\ensuremath{-}(D\ensuremath{-}1)/2}\mathrm{ln}r$ 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 $D\ensuremath{-}1$ 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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5123cbc2951c2b7ffd4a7487c2d895e2c2cd543b

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Citations in the corpus

Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, methodology): “When W(α) ∝ α3, however, G is larger and corresponds to the conformal isometry group of the Einstein static universe, G ∼= O(3, 2) [3, 12].”
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, background): “and charge generators We first recall the standard situation, from which we shall depart in the presence of a scalar field.”
Towards a Big Crunch Dual (2004, background): “Asymptotic solutions of this form can similarly be regarded as having AdS invariant boundary conditions provided β = α(f − 2 d lnα) [6, 8].”
Black holes with scalar hair and asymptotics in N = 8 supergravity (2004, result): “Note :Today, the paper [36] appeared on hep-th, which contains results that overlap with some of those presented in section 2 of this paper.”
Boundary conditions and dualities: vector fields in AdS/CFT (2006, background): “One may further show that all such boundary conditions remain valid when the scalar field is coupled to gravity; see [31] for a general analysis and [32, 33, 34, 35, 36, 37] for direct calculations.”
Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions (2006, background): “…a solution g, one can furthermore prove • for n ≥ 3, that all n− 2 forms that are closed for all solutions h of the linearized theory are given, on solutions h, by kξ for some Killing vector ξ, up to d exact n− 2 forms which do not contribute to the integrals [15, 17, 18], • if ξ1, ξ2 are Killing…”
Holographic anatomy of fuzzballs (2006, background): “presented (in a different coordinate system) in [ 46 ] and the form of the counterterm was”
Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, background): “It was later realized [320, 321] that even more general quantizations are possible in which the modes used to build the physical states have both A and B nonzero, with a relation between the two that ensures that the asymptotic symmetries of AdS are preserved [322,323].”
Effective holographic theories for low-temperature condensed matter systems (2010, background): “To this gravitational contribution, one must add a scalar term, [75, 65, 66],”
Symmetries of holographic minimal models (2011, background): “The case M(2) = M(2) BF, or λ = 0 in the dual CFT, may allow for interesting modifications because the scalars have relaxed behavior at infinity [42, 43].”
Exact black hole solution with a minimally coupled scalar field (2004, background): “This is a generic effect observed for scalar fields with a self-interacting potential unbounded form below in asymptotically AdS spacetimes [5, 27 , 28, 10].”