Entanglement Entropy for Singular Surfaces

TL;DR

This work investigates entanglement entropy for regions whose boundaries are geometrically singular in higher dimensions using holographic AdS/CFT techniques. By computing minimal-surface areas in bulk spacetimes, the authors uncover new universal contributions to EE that depend on the type of singularity (kink, cone, crease), the dimensionality, and the curvature of the singular locus. In particular, cones in even spacetime dimensions exhibit a log^2(delta) term with coefficients tied to central charges (e.g., c in d=4), while cones in odd dimensions feature a log(delta) term; extended singularities show universal terms only when the locus is curved and even-dimensional, with precise GB gravity results linking these contributions to boundary central charges. The findings illuminate how EE encodes detailed CFT data through singular geometries and suggest paths to extracting central charges from EE, while also highlighting regulator and conformal-map subtleties that warrant further study.

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.