Killing Superalgebras in 2 Dimensions

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 Poincaré) 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.

previously appeared in earlier form as part of the author's PhD thesis at https://era.ed.ac.uk/handle/1842/41754