  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.
