Higher Curvature Gravity from Entanglement in Conformal Field Theories

TL;DR

This paper extends the holographic entanglement entropy framework to higher curvature gravity theories, establishing connections between spacetime equations, Wald entropy corrections, and CFT relative entropy without using the Euclidean replica trick.

Contribution

It unifies and generalizes results relating higher curvature gravity to entanglement entropy, deriving key dualities and equations without the Euclidean replica trick.

Findings

Higher curvature gravity satisfies Einstein equations up to second order.

Holographic entanglement entropy includes Wald entropy plus extrinsic curvature corrections.

CFT relative entropy corresponds to gravitational canonical energy in higher curvature theories.

Abstract

By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically AdS spacetime computes the entanglement entropies of ball-shaped regions in a CFT using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around AdS; (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by Wald entropy plus a particular correction term involving extrinsic curvatures; (iii) CFT relative entropy is dual to gravitational canonical energy (also in higher curvature theories of gravity). Especially for the second point, our novel derivation of this previously known statement does not involve the Euclidean replica trick.