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

Abstract

The entanglement entropy for smooth regions $\mathcal{A}$ 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 $\mathcal{A}$, 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 $\mathcal{A}$, if equal scale ratios are chosen for the limiting procedure.

arXiv comment8 pages, 1 figure, Some sentences added in the conclusions section, version as appeared in PLB

References in corpus (5)

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• Entanglement entropy, conformal invariance and extrinsic geometry
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Cited by in corpus (6)

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• IR dynamics and entanglement entropy
• Observations on BPS observables in 6d
• On a new type of divergence for spiky Wilson loops and related entanglement entropies