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

The entanglement entropy for smooth regions A has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional log2 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 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 A, if equal scale ratios are chosen for the limiting procedure.