On the logarithmic divergent part of entanglement entropy, smooth versus singular regions

Understand

The entanglement entropy for smooth regions $\cal A$ has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional $\log ^2$ term.

• Comparing the coefficient of this extra term, obtained by direct holographic calculation for an infinite cone, with the corresponding limiting case for the shape dependent coefficient for a regularised cone, a mismatch by a factor two has been observed in the literature.
• We discuss several aspects of this issue.
• In particular a regularisation of $\cal A$, intrinsically delivered by the holographic picture, is proposed and applied to an example of a compact region with two conical singularities.