Universal Structure of Covariant Holographic Two-Point Functions In Massless Higher-Order Gravities

Abstract

We consider massless higher-order gravities in general $D=d+1$ dimensions, which are Einstein gravity extended with higher-order curvature invariants in such a way that the linearized spectrum around the AdS vacua involves only the massless graviton. We derive the covariant holographic two-point functions and find that they have a universal structure. In particular, the theory-dependent overall coefficient factor ${\mathcal{C}}_T$ can be universally expressed by $(d-1){\mathcal{C}}_T=\ell (\partial a/\partial \ell )$, where $a$ is the holographic $a$-charge and $\ell$ is the AdS radius. We verify this relation in quasi-topological Ricci polynomial, Einstein-Gauss-Bonnet, Einstein-Lovelock and Einstein cubic gravities. In $d=4$, we also find an intriguing relation between the holographic $c$ and $a$ charges, namely $c=\frac{1}{3}\ell (\partial a/\partial \ell )$, which also implies ${\mathcal{C}}_T=c$.

latex, 31 pages, typos corrected

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