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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.19923 |
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| _version_ | 1866914411207196672 |
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| author | Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea |
| author_facet | Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea |
| contents | This paper is a contribution to the supersymmetry gap problem for supergravity backgrounds $(M,g,F)$ in $11$ dimensions. We study restrictions on the curvature of $(M,g,F)$ and, using the bijective correspondence between the space of certain filtered deformations of Lie superalgebras and the space of highly supersymmetric supergravity backgrounds, we establish the following general rigidity result: if the $4$-form $F$ has rank $\operatorname{rk}(F)\leq 6$, Euclidean support, and the space $\mathfrak{k}_{\bar 1}$ of Killing spinors has dimension $\dim\mathfrak{k}_{\bar 1}> 26$ then $(M,g,F)$ is locally isometric to the maximally supersymmetric Minkowski spacetime or Freund Rubin background $\mathrm{AdS}_7\times\mathrm{S}^4$. The same rigidity result but with finer estimates on $\dim\mathfrak{k}_{\bar 1}$ is provided for certain types of $\mathfrak k_{\bar 1}$ and specific orbits of the $4$-form under the action of the Lorentz group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some rigidity results for supergravity backgrounds in 11 dimensions Di Bella, Emanuele de Graaf, Willem A. Santi, Andrea High Energy Physics - Theory Differential Geometry Representation Theory This paper is a contribution to the supersymmetry gap problem for supergravity backgrounds $(M,g,F)$ in $11$ dimensions. We study restrictions on the curvature of $(M,g,F)$ and, using the bijective correspondence between the space of certain filtered deformations of Lie superalgebras and the space of highly supersymmetric supergravity backgrounds, we establish the following general rigidity result: if the $4$-form $F$ has rank $\operatorname{rk}(F)\leq 6$, Euclidean support, and the space $\mathfrak{k}_{\bar 1}$ of Killing spinors has dimension $\dim\mathfrak{k}_{\bar 1}> 26$ then $(M,g,F)$ is locally isometric to the maximally supersymmetric Minkowski spacetime or Freund Rubin background $\mathrm{AdS}_7\times\mathrm{S}^4$. The same rigidity result but with finer estimates on $\dim\mathfrak{k}_{\bar 1}$ is provided for certain types of $\mathfrak k_{\bar 1}$ and specific orbits of the $4$-form under the action of the Lorentz group. |
| title | Some rigidity results for supergravity backgrounds in 11 dimensions |
| topic | High Energy Physics - Theory Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2603.19923 |