Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

Understand

We derive a general formula for renormalized entanglement entropy in even dimensional CFTs holographically dual to Einstein gravity in one dimension higher.

• In order to renormalize, we adapt the Kounterterm method to asymptotically locally AdS manifolds with conical singularities.
• On the gravity side, the computation considers extrinsic counterterms and the use of the replica trick a la Lewkowycz-Maldacena.
• The boundary counterterm B_d is shown to satisfy a key property, in direct analogy to the Euler density: when evaluated on a conically singular manifold, it decomposes into a regular part plus a codimension-2 version of itself located at the conical singularity.