Einstein and Yang-Mills implies conformal Yang-Mills
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908767169282048 |
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| author | Blitz, Samuel Gover, A. Rod Kopiński, Jarosław Waldron, Andrew |
| author_facet | Blitz, Samuel Gover, A. Rod Kopiński, Jarosław Waldron, Andrew |
| contents | There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension greater than or equal to six. We give a compact formula for these analogs and prove that they are a strict weakening of the Yang-Mills condition with respect to an Einstein metric. We also show that the conformal Yang-Mills condition for the tractor connection of an even dimensional conformal manifold is equivalent to vanishing of its Fefferman-Graham obstruction tensor. This result uses that the tractor connection on a Poincaré-Einstein manifold is itself Yang-Mills. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Einstein and Yang-Mills implies conformal Yang-Mills Blitz, Samuel Gover, A. Rod Kopiński, Jarosław Waldron, Andrew Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension greater than or equal to six. We give a compact formula for these analogs and prove that they are a strict weakening of the Yang-Mills condition with respect to an Einstein metric. We also show that the conformal Yang-Mills condition for the tractor connection of an even dimensional conformal manifold is equivalent to vanishing of its Fefferman-Graham obstruction tensor. This result uses that the tractor connection on a Poincaré-Einstein manifold is itself Yang-Mills. |
| title | Einstein and Yang-Mills implies conformal Yang-Mills |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.09975 |