Holographic Entanglement Entropy for the Most General Higher Derivative Gravity

TL;DR

The paper develops a comprehensive holographic entanglement entropy framework for the most general higher derivative gravity, introducing a generalized Wald entropy term and an entropy anomaly to account for extrinsic-curvature effects. It provides a formal HEE formula applicable to actions with curvature derivatives, and concretely derives exact results for several conical geometries, including six- and 2n-derivative theories. Checks against 4d CFT universal terms confirm the correctness of the approach, while a resolution of the HMS puzzle clarifies how derivative-of-curvature contributions reconcile Weyl-anomaly calculations with holography. The work also discusses splitting ambiguities in conical metrics and advocates the LM regularization as essential for matching holographic results, highlighting remaining open questions for higher-derivative splittings.

Abstract

The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the `anomaly of entropy' of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.