Einstein Gravity from Conformal Gravity in 6D

TL;DR

This paper demonstrates that six-dimensional conformal gravity can produce Einstein gravity solutions through specific boundary conditions, extending previous 4D results and revealing a deep connection between these theories.

Contribution

It generalizes Maldacena's 4D argument to 6D, showing how Einstein gravity emerges from conformal gravity via boundary conditions and invariants.

Findings

6D conformal gravity admits an Einstein sector.

Einstein solutions are obtained via generalized Neumann boundary conditions.

The equivalence simplifies understanding of 6D critical gravity solutions.

Abstract

We extend Maldacena's argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by taking generalized Neumann boundary conditions, the Conformal Gravity action reduces to the renormalized Einstein-AdS action. These restrictions are implied by the vanishing of the traceless Ricci tensor, which is the defining property of any Einstein spacetime. The equivalence between Conformal and Einstein gravity renders trivial the Einstein solutions of 6D Critical Gravity at the bicritical point.