Abstract
It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case.
Highlights
Evaluating the gravity action on-shell, the terms that contain negative powers of z will blow up at the cutoff
We can notice that the asymptotic form of the metric function (3.6) suggests that a difference between the Weyl and anti-de Sitter (AdS) curvature tensors (3.5) of a massive state in Lovelock AdS gravity is given as an power-expansion of the quantity (μ/rD−1)1/K
We have extended the concept of Conformal Mass to any branch of Lovelock AdS gravity, as long as the corresponding vacuum is non-degenerate
Summary
Higher-dimensional gravity theories in AdS space with second-order equations of motion are of particular interest for holographic purpose. They represent a generalization of General Relativity and depend on a number parameters which provide a richer playground for gauge/gravity duality applications. In order to see the higher-curvature terms as corrections to the Einstein-Hilbert AdS gravity, we fix the first coupling constants as α1 = 1 and α0 = −2Λ, where Λ = −(D − 1)(D − 2)/2 2 is the cosmological constant expressed in terms of the AdS radius. Higher-order curvature terms change the bare AdS radius of Einstein-Hilbert gravity, , to the effective AdS radius, eff. Such that each root of ∆ defines a different sector in the theory
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