Universal entanglement for higher dimensional cones

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 Omega, codified in a function a((d))(Omega). In arXiv : 1505 . 04804, we proposed that for three-dimensional conformal field theories, the coefficient sigma((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 de fine a generalized coefficient sigma((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 sigma((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 Renyi entropies, which we show passes several consistency checks in d - 4 and 6.