# Universal structure of covariant holographic two-point functions in massless higher-order gravities

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## 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 \( \left(d - 1\right){\mathcal{C}}_T = \ell \left(\partial a/\partial \ell \right) \), where *a* is the holographic *a*-charge and *ℓ* 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 \( c=\frac{1}{3}\ell \left(\partial a/\partial \ell \right) \), which also implies \( {\mathcal{C}}_T=c \).

## Keywords

AdS-CFT Correspondence Classical Theories of Gravity## Notes

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