Entanglement Entropy for Singular Surfaces

TL;DR

This paper investigates how singular boundary geometries in higher-dimensional conformal field theories affect entanglement entropy, revealing universal contributions linked to the geometry and central charges via holographic methods.

Contribution

It identifies new universal terms in entanglement entropy arising from singular boundary surfaces in higher dimensions, including quadratic log terms in even dimensions and linear log terms in odd dimensions.

Findings

Conical singularities introduce universal logarithmic contributions to entanglement entropy.

In four dimensions, the coefficient of the quadratic log term is proportional to the central charge 'c'.

Extended singularities can produce similar universal terms depending on their geometry.

Abstract

We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.