Higher derivative corrections in holographic Zamolodchikov–Polchinski theorem

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 Poincaré 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 twodimensional field theoretic proof of the both.