Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity

Abstract

We discuss various aspects of rigid supersymmetry within minimal N=1 off-shell supergravity using the old and new minimal formulations both in Lorentzian and Euclidean signatures. In particular, we construct all rigid supersymmetry backgrounds with a hypersurface orthogonal Killing vector. In the Lorentzian signature we show that AdS_4 provides a rigid supersymmetric background in both formulations albeit with different amounts of preserved supersymmetry. In the Euclidean signature we find new backgrounds of the old-minimal supergravity, including squashed four-spheres and a half-BPS version of flat space.

40 pages: v2 References added, typos corrected

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• Rigid 6D supersymmetry and localization
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• Higher Derivative Supergravities in Diverse Dimensions
• Rigid 4D N=2 supersymmetric backgrounds and actions
• An introduction to supersymmetric field theories in curved space
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• Killing superalgebras for Lorentzian four-manifolds
• Superconformal quantum field theory in curved spacetime
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• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
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• Ten-dimensional lifts of global supersymmetry on curved spaces
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• On N=1 partition functions without R-symmetry
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension
• Holographic origin of $a$-maximization and higher-derivative AdS${}_5$/CFT${}_4$