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The entanglement entropy for smooth regions $\cal A$ has a logarithmicdivergent contribution with a shape dependent coefficient and that for regionswith conical singularities an additional $\log ^2$ term. Comparing thecoefficient of this extra term, obtained by direct holographic calculation foran infinite cone, with the corresponding limiting case for the shape dependentcoefficient for a regularised cone, a mismatch by a factor two has beenobserved in the literature. We discuss several aspects of this issue. Inparticular a regularisation of $\cal A$, intrinsically delivered by theholographic picture, is proposed and applied to an example of a compact regionwith two conical singularities. Finally, the mismatch is removed in all studiedregularisations of $\cal A$, if equal scale ratios are chosen for the limitingprocedure.

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