Einstein gravity from Conformal Gravity in 6D

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.

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Correspondence to Ignacio J. Araya.

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Anastasiou, G., Araya, I.J. & Olea, R. Einstein gravity from Conformal Gravity in 6D. J. High Energ. Phys. 2021, 134 (2021). https://doi.org/10.1007/JHEP01(2021)134

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Keywords

  • AdS-CFT Correspondence
  • Classical Theories of Gravity
  • Conformal and W Symmetry