8D conformal gravity with Einstein sector, and its relation to the Q-curvature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911255295426560 |
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| author | Boulanger, Nicolas Rovere, Davide |
| author_facet | Boulanger, Nicolas Rovere, Davide |
| contents | 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01368 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 8D conformal gravity with Einstein sector, and its relation to the Q-curvature Boulanger, Nicolas Rovere, Davide High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry 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 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. |
| title | 8D conformal gravity with Einstein sector, and its relation to the Q-curvature |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2511.01368 |