  We study higher derivative corrections in holographic dual of
Zamolodchikov-Polchinski theorem that states the equivalence between scale
invariance and conformal invariance in unitary d-dimensional Poincare invariant
field theories. From the dual holographic perspective, we find that a
sufficient condition to show the holographic theorem is the generalized strict
null energy condition of the matter sector in effective (d+1)-dimensional
gravitational theory. The same condition has appeared in the holographic dual
of the "c-theorem" and our theorem suggests a deep connection between the two,
which was manifested in two-dimensional field theoretic proof of the both.
