Generalized entropy and higher derivative Gravity

TL;DR

The paper extends holographic entanglement entropy to curvature-squared gravity by deriving a generalized entangling functional that adds an extrinsic-curvature quadratic term to Wald entropy, with a coefficient given by the second derivative of the Lagrangian with respect to the Riemann tensor. Using a replica-trick framework and conical singularities, the authors show that the standard Wald term emerges for zero extrinsic curvature, while nonzero extrinsic curvature yields a finite correction captured by a new entropy functional; in Gauss–Bonnet gravity this reduces precisely to the Jacobson–Myers functional. The result provides a principled method to compute holographic entanglement in higher-derivative theories and connects to broader prescriptions such as Dong’s, with implications for higher-dimensional CFT entanglement structure. The work also discusses regulator choices, potential Lorentzian extensions, and future directions for applying the generalized entropy to gravitational and field-theoretic contexts.

Abstract

We derive an extension of the Ryu-Takayanagi prescription for curvature squared theories of gravity in the bulk, and comment on a prescription for more general theories. This results in a new entangling functional, that contains a correction to Wald's entropy. The new term is quadratic in the extrinsic curvature. The coefficient of this correction is a second derivative of the lagrangian with respect to the Riemann tensor. For Gauss-Bonnet gravity, the new functional reduces to Jacobson-Myers'.