A Note on Holographic Weyl Anomaly and Entanglement Entropy

TL;DR

This paper presents a simplified method for deriving holographic Weyl anomalies and entanglement entropy in higher derivative gravity theories, successfully validating Dong's proposal for 4d conformal field theories without relying on equations of motion.

Contribution

It introduces a general approach to compute holographic Weyl anomalies and proposes a formula for entanglement entropy in higher derivative gravity, confirming Dong's proposal for 4d CFTs.

Findings

Derived holographic Weyl anomaly without using equations of motion.

Proposed a formula for holographic entanglement entropy in higher derivative gravity.

Confirmed that Dong's proposal correctly captures the universal entanglement entropy term for 4d CFTs.

Abstract

We develop a general approach to simplify the derivation of the holographic Weyl anomaly. As an application, we derive the holographic Weyl anomaly from general higher derivative gravity in asymptotically $AdS_{5}$ and $AdS_{7}$. Interestingly, to derive all the central charges of 4d and 6d CFTs, we make no use of equations of motion. Following Myers' idea, we propose a formula of holographic entanglement entropy for higher derivative gravity in asymptotically $AdS_5$. Applying this formula, we obtain the correct universal term of entanglement entropy for 4d CFTs. It turns out that our formula is the leading term of Dong's proposal in asymptotically $AdS_5$. Since only the leading term contributes to the universal log term, we actually prove that Dong's proposal yields the correct universal term of entanglement entropy for 4d CFTs. This is a nontrivial test of Dong's proposal.