  We calculate the two-point function of the trace of the stress tensor in
holographic renormalization group flows between pairs of conformal field
theories. We show that the term proportional to the momentum squared in this
correlator gives the change of the central charge between fixed points in d=2
and in d>2 it gives the holographic entanglement entropy for a planar region.
This can also be seen as a holographic realization of the Adler-Zee formula for
the renormalization of Newton's constant. Holographic regularization is found
to provide a perfect match of the finite and divergent terms of the sum rule,
and it is analogous to the regularization of the entropy in terms of mutual
information. Finally, we provide a general proof of reflection positivity in
terms of stability of the dual bulk action, and discuss the relation between
unitarity constraints, the null energy condition and regularity in the interior
of the gravity solution.
