Noether-Wald charges in six-dimensional Critical Gravity

Giorgos Anastasiou, Ignacio J. Araya, Cristóbal Corral, Rodrigo Olea

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It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

Original languageEnglish
Article number156
JournalJournal of High Energy Physics
Issue number7
Publication statusPublished - Jul 2021


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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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