Abstract
We study curved-space rigid supersymmetry for two-dimensional \( \mathcal{N} \) = (2, 2) supersymmetric fields theories with a vector-like R-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be viewed as holomorphic sections of particular complex line bundles over Euclidean space-time, which severely restricts the allowed supersymmetric couplings on compact orientable Riemann surfaces without boundaries. For genus g > 1, the only consistent non-singular couplings are the ones dictated by the topological A-twist. On spaces with S 2 topology, there exist additional supersymmetric backgrounds with m = 0 or ±1 unit of flux for the R-symmetry gauge field. The m = −1 case includes the Ω-background on the sphere. We also systematically work out the curved-space supersymmetry multiplets and supersymmetric Lagrangians.
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Closset, C., Cremonesi, S. Comments on \( \mathcal{N} \) = (2, 2) supersymmetry on two-manifolds. J. High Energ. Phys. 2014, 75 (2014). https://doi.org/10.1007/JHEP07(2014)075
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DOI: https://doi.org/10.1007/JHEP07(2014)075