As we have already seen, in even dimensions, there typically appears a logarithmic term in the entanglement entropy. This term is universal in the sense that it does not depend on the scheme, which is used to regularize the UV divergences. In conformal field theories the logarithmic terms in the entropy are closely related to the conformal anomaly. In this section we discuss in detail this aspect and formulate precisely the relation between entanglement entropy and conformal anomalies.
Consider a conformal field theory in spacetime dimensions. As we have discussed throughout this review the most efficient way to calculate the corresponding entanglement entropy for a non-extremal black hole is to introduce a small angle deficit at the horizon surface , compute the effective action on a manifold with a singular surface and then apply the replica formula and obtain from it the entanglement entropy. In dimensions the effective action has the general structure
An important property of the expansion (269) for a quantum field theory, which classically is conformally invariant, is that the logarithmic term is conformally invariant (see  and references therein),
Living Rev. Relativity 14, (2011), 8
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