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arXiv · 2410.01765

Killing Superalgebras in 2 Dimensions

Andrew D. K. Beckett
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Abstract

We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages, arXiv:2409.11306]. We compute the Spencer cohomology group $\mathsf{H}^{2,2}(\mathfrak{s}_-;\mathfrak{s})$ and filtered deformations of the non-chiral flat model (Euclidean and Poincar\'e) superalgebra $\mathfrak{s}$ for various Dirac currents and show these arise as Killing superalgebras for (imaginary) geometric Killing and skew-Killing spinors in both Riemannian and Lorentzian signature.

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Andrew D. K. Beckett. 2024-10-02. Killing Superalgebras in 2 Dimensions. https://doi.org/10.3842/sigma.2025.082

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