Higher derivative corrections in holographic Zamolodchikov–Polchinski theorem

Abstract

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.