Entanglement entropy due to near horizon degrees of freedom

TL;DR

This paper analytically derives the entanglement entropy for a free massless scalar field across a spherical surface, highlighting a leading area law term and a positive logarithmic correction, with extensions to higher dimensions.

Contribution

It provides an analytical derivation of entanglement entropy considering near horizon degrees of freedom, including subleading corrections and higher-dimensional generalizations.

Findings

Entropy proportional to the surface area

Identification of a positive logarithmic correction

Extension of analysis to higher dimensions

Abstract

Assuming that the dominant contribution, to the entropy due to entanglement across a spherical hypersurface, comes from the near horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski spacetime across a spherical entangling surface. The resulting entanglement entropy is found to be proportional to the entangling surface as expected. A logarithmic subleading term with positive coefficient is also found through numerical computation. We have extended the analysis to higher dimensions as well.