Towards a derivation of holographic entanglement entropy

TL;DR

This paper derives holographic entanglement entropy for spherical regions by conformally mapping the boundary CFT to a hyperbolic space, relating entanglement to black hole horizon entropy, and discusses universal contributions in even dimensions.

Contribution

It provides a new derivation of holographic entanglement entropy using conformal mappings and relates it to black hole thermodynamics, extending understanding beyond holography.

Findings

Entanglement entropy mapped to black hole horizon entropy.

Universal contribution linked to A-type trace anomaly.

Method applicable to spherical entangling surfaces.

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.