A c-theorem for the 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 obstacle the naive generalizations of the entropic c-theorem to higher dimensions.