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arXiv · 2508.14240

On a Grassmann odd analogue of Carrollian Manifolds

Andrew James Bruce
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Abstract

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 In\"on\"u--Wigner contraction of the supertranslation algebra on standard superspace $\mathbb{R}^{4|4}$.

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Andrew James Bruce. 2025-08-19. On a Grassmann odd analogue of Carrollian Manifolds. https://arxiv.org/abs/2508.14240

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