  Using the AdS/CFT correspondence, we examine entanglement entropy for a
boundary theory deformed by a relevant operator and establish two results. The
first is that if there is a contribution which is logarithmic in the UV
cut-off, then the coefficient of this term is independent of the state of the
boundary theory. In fact, the same is true of all of the coefficients of
contributions which diverge as some power of the UV cut-off. Secondly, we show
that the relevant deformation introduces new logarithmic contributions to the
entanglement entropy. The form of some of these new contributions is similar to
that found recently in an investigation of entanglement entropy in a free
massive scalar field theory [1].
