Abstract
The entanglement entropy of a generic d-dimensional conformal field theory receives a regulator independent contribution when the entangling surface 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 (3) characterizing the limit where the surface becomes smooth is proportional to the central charge C T appearing in the two-point function of the stress tensor. In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions. In particular, we define a generalized coefficient σ (d) to characterize the almost smooth limit of a (hyper)conical singularity in entangling surfaces in higher dimensions. We show then that this coefficient is universally related to C T for general holographic theories and provide a general formula for the ratio σ (d) /C T 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 6.
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Bueno, P., Myers, R.C. Universal entanglement for higher dimensional cones. J. High Energ. Phys. 2015, 1–24 (2015). https://doi.org/10.1007/JHEP12(2015)168
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DOI: https://doi.org/10.1007/JHEP12(2015)168