## Abstract

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 language | English |
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Article number | 156 |

Journal | Journal of High Energy Physics |

Volume | 2021 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2021 |

## Keywords

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

## ASJC Scopus subject areas

- Nuclear and High Energy Physics