On a Grassmann odd analogue of Carrollian Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909981933043712 |
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| author | Bruce, Andrew James |
| author_facet | Bruce, Andrew James |
| contents | We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension $n|1$ with an even degenerate metric such that the kernel is generated by a non-singular odd vector field that is a supersymmetry generator. Alongside other results, we establish that the reduced manifold is a pseudo-Riemannian manifold, and show that compatible affine connections always exist, albeit they must carry torsion. As a physically relevant example, we examine an Inönü--Wigner contraction of the supertranslation algebra on standard superspace $\mathbb{R}^{4|4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Grassmann odd analogue of Carrollian Manifolds Bruce, Andrew James Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 58A50, 58C50, 53B05 We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension $n|1$ with an even degenerate metric such that the kernel is generated by a non-singular odd vector field that is a supersymmetry generator. Alongside other results, we establish that the reduced manifold is a pseudo-Riemannian manifold, and show that compatible affine connections always exist, albeit they must carry torsion. As a physically relevant example, we examine an Inönü--Wigner contraction of the supertranslation algebra on standard superspace $\mathbb{R}^{4|4}$. |
| title | On a Grassmann odd analogue of Carrollian Manifolds |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 58A50, 58C50, 53B05 |
| url | https://arxiv.org/abs/2508.14240 |