Second-order Lovelock Gravity from Entanglement in Conformal Field Theories

TL;DR

This paper demonstrates that assumptions linking holographic entanglement entropy to the boundary CFT can lead to second-order Lovelock gravity in the bulk, showing the holographic area law alone cannot uniquely determine the bulk theory beyond Einstein gravity.

Contribution

It generalizes previous work to show that second-order Lovelock gravity also satisfies the holographic entanglement entropy area law, indicating non-uniqueness in bulk theories derived from RT assumptions.

Findings

Lovelock entropy obeys an area law up to second order.

RT assumptions do not uniquely determine the bulk gravity theory.

Second-order Lovelock gravity can emerge from holographic entanglement considerations.

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.