A Note on Holographic Weyl Anomaly and Entanglement Entropy

TL;DR

This work addresses the challenge of deriving holographic Weyl anomalies for general higher-derivative gravity in AdS/CFT. It introduces a curvature-expansion approach that isolates anomaly-relevant terms, enabling universal formulas for the 4d and 6d Weyl anomalies without solving bulk equations of motion. The authors provide explicit expressions for the central charges in several theories (Love-Lock, $f(R)$, critical gravity, and curvature-derivative gravities) and verify consistency with known results across dimensions. Additionally, they propose a holographic entanglement entropy formula for asymptotically AdS5, showing it reproduces the universal log term and corresponds to the leading term of Dong's entropy functional, yielding a nontrivial test of Dong's proposal. The results advance practical tools for analyzing holographic anomalies and entanglement in broad gravity theories, with potential extensions to higher dimensions and more general actions.

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.