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<p>We first streamline the construction of the unique six-dimensional conformal gravity action found by Lü, 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 <i>Q</i>-curvature and the Fefferman-Graham obstruction tensor, to conjecture that on every even-dimensional space there exists a unique — up to boundary terms — conformally-invariant gravity theory that is extremised by Einstein metrics.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月9日

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  • Nicolas Boulanger,
  • Davide Rovere

摘要

We first streamline the construction of the unique six-dimensional conformal gravity action found by Lü, 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 conjecture that on every even-dimensional space there exists a unique — up to boundary terms — conformally-invariant gravity theory that is extremised by Einstein metrics.