Universal entanglement for higher dimensional cones

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The entanglement entropy of a generic d-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle Ω, codified in a function a⁽ᵈ⁾(Ω). In arXiv:1505.04804, we proposed that for three-dimensional conformal field theories, the coefficient σ characterizing the smooth surface limit of such contribution (Ω→ π) equals the stress tensor two-point function charge Cₜ, up to a universal constant. In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions. In particular, we show that a generalized coefficient σ⁽ᵈ⁾ can be defined for (hyper)conical entangling regions in the almost smooth surface limit, and that this coefficient is universally related to Cₜ for general holographic theories, providing a general formula for the ratio σ⁽ᵈ⁾/Cₜ in arbitrary dimensions. We conjecture that the latter ratio is universal for general CFTs. Further, based on our recent results in arXiv:1507.06997, we propose an extension of this relation to general Rényi entropies, which we show passes several consistency checks in d=4 and d=6.