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

TL;DR

This paper uncovers a universal structure in covariant holographic two-point functions for massless higher-order gravities, linking key coefficients to the holographic $a$-charge and verifying this across various gravity theories.

Contribution

It derives a universal relation for the coefficient $ ext{C}_T$ in holographic two-point functions in massless higher-order gravities, connecting it to the holographic $a$-charge and confirming it in multiple gravity models.

Findings

Universal structure of two-point functions identified.

Coefficient $ ext{C}_T$ expressed via $a$-charge and AdS radius.

Relation between $c$ and $a$ charges in $d=4$ confirmed.

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 $\mathcal{C}_T=c$.