Entanglement entropy of round spheres

TL;DR

This paper proposes a correspondence between the logarithmic terms in entanglement entropy for spherical regions in conformal field theories and extreme black holes, supported by explicit calculations for scalar fields.

Contribution

It introduces a novel connection between entanglement entropy in conformal field theories and black hole physics, specifically relating the logarithmic terms in different geometries.

Findings

Logarithmic terms in entanglement entropy are identical for spheres and extreme black holes.

Explicit calculations for scalar fields support the proposed equivalence.

Discussion of implications for 4d conformal field theories and the brick wall model.

Abstract

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a $(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near-horizon geometry of the latter is $H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the ``brick wall'' model of 't Hooft. The case of generic 4d conformal field theory is discussed.