  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. Finally, the mismatch is removed in all studied
regularisations of $\cal A$, if equal scale ratios are chosen for the limiting
procedure.

High Energy Physics - Theory;Quantum Physics