Entanglement entropy of round spheres

TL;DR

The paper shows that the universal logarithmic term in entanglement entropy for a round $(d-2)$-sphere in flat space coincides with that of an extreme black hole by mapping to the near-horizon geometry $H_2\times S_{d-2}$ and computing via conical-singularity and heat-kernel methods. It demonstrates explicit results for a conformal scalar in various even dimensions and argues that, in 4d, the logarithmic term is governed by the type-A conformal anomaly with $s_0^{ext}=A\pi^2$, while Schwarzschild geometry involves $(A-B)\pi^2$. The findings connect entanglement entropy, brick-wall regularization, and holographic prescriptions, reinforcing the AdS/CFT picture and highlighting the universality of the logarithmic term across conformally related settings. These results have implications for understanding black hole entropy from quantum field theory, and they suggest that flat-space entanglement measurements could shed light on holographic and microscopic descriptions of gravity.

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.