A Note on Holographic Weyl Anomaly and Entanglement Entropy

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 $Ad{S}_5$ and $Ad{S}_7$. 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 $Ad{S}_5$. 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 $Ad{S}_5$. 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.

20 pages, no figures, accepted by Classical and Quantum Gravity, prove that Dong's proposal [arXiv: arXiv:1310.5713] gives the correct universal term of entanglement entropy for 4d CFTs

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