Second-order Lovelock gravity from entanglement in conformal field theories
Second-order Lovelock gravity from entanglement in conformal field theories
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DOI：
10.1103/physrevd.104.126018
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发表时间：
2019-12
影响因子：
5
通讯作者：
C. Fan;G. Nave;P. Phillips
中科院分区：
文献类型：
--
作者：
C. Fan;G. Nave;P. Phillips
全息纠缠熵和热力学第一定律被认为可以解读整体的引力理论。特别是，假设Ryu-Takayanagi (RT) \cite{ryu-takayanagi}公式适用于CFT真空态边界上的球形区域，这意味着\cite{Nonlinear-Faulkner}通过二阶扰动等效于爱因斯坦引力的体引力理论。在本文中，我们证明了同样的假设也可以产生二阶洛夫洛克引力。具体地说，我们在\cite{Nonlinear-Faulkner}中推广了这个过程，通过二阶摄动理论证明，那里的参数也适用于洛夫洛克引力，在洛夫洛克中使用沃尔德公式\cite{Wald_noether}计算的熵也服从面积定律（至少到二阶）。由于洛夫洛克引力的二阶摄动方程一般不同于爱因斯坦-希尔伯特作用的二阶摄动方程，我们的工作表明，全息面积定律不能确定一个独特的体理论，即使是在球形区域上只假设RT的二阶摄动。期望所有子区域上的RT都能编码渐近AdS时空上的完整非线性爱因斯坦方程。
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.