Towards a derivation of holographic entanglement entropy

TL;DR

The paper provides a nonreplica-trick derivation of holographic entanglement entropy for spherical entangling surfaces by mapping the boundary CFT to a hyperbolic geometry where the vacuum becomes thermal. This thermal entropy is then computed holographically as the horizon entropy of a bulk topological black hole, yielding a general result applicable to arbitrary covariant bulk actions and reproducing the Ryu–Takayanagi prescription in Einstein gravity. In even dimensions, the universal logarithmic term in the entanglement entropy is shown to be governed by the A-type trace anomaly (the central charge a), while in odd dimensions the universal piece is tied to the sphere partition function. The work also clarifies regulator relations (UV/IR matching) inherent in conformal mappings and extends the CFT analysis to cylindrical backgrounds, tying together holographic and field-theoretic perspectives on entanglement entropy.

Abstract

We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.