Higher derivative corrections in holographic Zamolodchikov-Polchinski theorem

TL;DR

This paper explores how higher derivative corrections in holographic duals influence the equivalence of scale and conformal invariance, revealing a deep connection with the holographic c-theorem through the null energy condition.

Contribution

It demonstrates that a generalized strict null energy condition ensures the holographic Zamolodchikov-Polchinski theorem holds even with higher derivative corrections.

Findings

Null energy condition is key to the holographic theorem

Connection between the Zamolodchikov-Polchinski and c-theorems

Higher derivative corrections do not break the equivalence

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 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.