Abstract
We classify all \( \mathcal{N}=2 \) rigid supersymmetric backgrounds in four dimensions with both Lorentzian and Euclidean signature that preserve eight real supercharges, up to discrete identifications. Among the backgrounds we find specific warpings of \( {S}^3\times \mathrm{\mathbb{R}} \) and \( {\mathrm{AdS}}_3\times \mathrm{\mathbb{R}} \), AdS2 × S 2 and H 2 × S 2 with generic radii, and some more exotic geometries. We provide the generic two-derivative rigid vector and hypermultiplet actions and analyze the conditions imposed on the special Kähler and hyperkähler target spaces.
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Butter, D., Inverso, G. & Lodato, I. Rigid 4D \( \mathcal{N}=2 \) supersymmetric backgrounds and actions. J. High Energ. Phys. 2015, 88 (2015). https://doi.org/10.1007/JHEP09(2015)088
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DOI: https://doi.org/10.1007/JHEP09(2015)088