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arXiv · 2511.01368

8D conformal gravity with Einstein sector, and its relation to the Q-curvature

Nicolas Boulanger·Davide Rovere
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Abstract

We first streamline the construction of the unique six-dimensional conformal gravity action found by L\"u, Pang and Pope, that admits Einstein metrics as solutions to the field equations. We then prove that there exists a unique eight-dimensional conformal gravity action that admits Einstein metrics as solutions to the field equations, and explicitly build the corresponding action. Finally, we relate these results to Branson's Q-curvature and the Fefferman-Graham obstruction tensor, to conclude that on every even-dimensional space there exists a unique -- up to boundary terms -- conformally-invariant gravity theory that is extremised by Einstein metrics.

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Nicolas Boulanger, Davide Rovere. 2025-11-03. 8D conformal gravity with Einstein sector, and its relation to the Q-curvature. https://arxiv.org/abs/2511.01368

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