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

Abstract

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 $$ {\mathcal{C}}_T $$ C T can be universally expressed by $$ \left(d - 1\right){\mathcal{C}}_T = \ell \left(\partial a/\partial \ell \right) $$ d − 1 C T = ℓ ∂ a / ∂ ℓ , 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 $$ c=\frac{1}{3}\ell \left(\partial a/\partial \ell \right) $$ c = 1 3 ℓ ∂ a / ∂ ℓ , which also implies $$ {\mathcal{C}}_T=c $$ C T = c .