Ac-theorem for entanglement entropy

The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c -theorem for the entanglement entropy in (1+1) dimensions. We present a simple derivation of this theorem and compare the associated c -functions with the Zamolodchikov's ones for the case of free fields. We discuss the various difficulties which are obstacles to the naive generalizations of the entropic c -theorem to higher dimensions.