Abstract
Holographic entanglement entropy and the first law of thermodynamics are believed to decode the gravity theory in the bulk. In particular, assuming the Ryu-Takayanagi (RT)\cite{ryu-takayanagi} formula holds for ball-shaped regions on the boundary around CFT vacuum states implies\cite{Nonlinear-Faulkner} a bulk gravity theory equivalent to Einstein gravity through second-order perturbations. In this paper, we show that the same assumptions can also give rise to second-order Lovelock gravity. Specifically, we generalize the procedure in \cite{Nonlinear-Faulkner} to show that the arguments there also hold for Lovelock gravity by proving through second-order perturbation theory, the entropy calculated using the Wald formula\cite{Wald_noether} in Lovelock also obeys an area law (at least up to second order). Since the equations for second-order perturbations of Lovelock gravity are different in general from the second-order perturbation of the Einstein-Hilbert action, our work shows that the holographic area law cannot determine a unique bulk theory even for second-order perturbations assuming only RT on ball-shaped regions. It is anticipated that RT on all subregions is expected to encode the full non-linear Einstein equations on asymptotically AdS spacetimes.
Highlights
While the anti–de Sitter (AdS)=CFT correspondence can be construed broadly as a mechanism for constructing a dual representation of a conformal field theory (CFT) in terms of gravity, it implies an equivalence between the states in both theories
We show in this paper that Lovelock [14] gravity can emerge from entanglement á la RT [1,4], a fact that seems to indicate that string-theoretic corrections to the bulk may go through Lovelock perturbations of vacuum anti–de Sitter (AdS)
In the conclusion section of this paper we show that in Lovelock holography, the JacobsonMyers formula for perturbations around vacuum AdS coincides with the RT formula up to second order as well, establishing that even the true holographic bulk Lovelock dual to a CFT is indistinguishable from the Einstein bulk dual, up to second order
Summary
While the AdS=CFT correspondence can be construed broadly as a mechanism for constructing a dual representation of a conformal field theory (CFT) in terms of gravity, it implies an equivalence between the states in both theories. We show in this paper that Lovelock [14] gravity can emerge from entanglement á la RT [1,4], a fact that seems to indicate that string-theoretic corrections to the bulk may go through Lovelock perturbations of vacuum anti–de Sitter (AdS) (which has the feature of satisfying both Einstein and Lovelock gravity) This is important because nonlinear curvature theories are commonplace in string-theoretic constructions and cosmology. Tgh12eþgP augk eξkcgo2uk.plTinhge function fðφÞ importance of nonlinear curvature theories is manifest in the string theoretic analysis of quantum bulk effects at the near horizon geometries of Lifshitz solutions. The effects of these quantum corrections is seen to imply a flow from the UV. Further generalizations have been made based on actions with higher-order curvatures [17]
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