Renormalized AdS action and Critical Gravity

TL;DR

This paper demonstrates that the renormalized AdS gravity action in even dimensions reduces on-shell to a polynomial in the Weyl tensor, with the leading term matching the coupling in Critical Gravity, revealing a deep connection between these theories.

Contribution

It establishes an equivalence between the renormalized AdS action and a Weyl tensor polynomial, linking it directly to Critical Gravity coupling constants.

Findings

On-shell equivalence of renormalized AdS action and Weyl polynomial

Leading term proportional to Weyl squared matches Critical Gravity coupling

Provides insight into the structure of AdS gravity in even dimensions

Abstract

It is shown that the renormalized action for AdS gravity in even spacetime dimensions is equivalent -on shell- to a polynomial of the Weyl tensor, whose first non-vanishing term is proportional to $Weyl^2$. Remarkably enough, the coupling of this last term coincides with the one that appears in Critical Gravity.