Supersymmetric Spacetimes from Curved Superspace

Abstract

We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitrary off-shell supergravity-matter couplings. Fourthly, all maximally supersymmetric Lorentzian spaces correspond to those off-shell supergravity backgrounds for which the Grassmann-odd components of the superspace torsion and curvature tensors vanish, while the Grassmann-even components of these tensors are annihilated by the spinor derivatives.

arXiv comment21 pages, Contribution to proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity," 3-21 September 2014, Corfu, Greece

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• Rigid 4D N=2 supersymmetric backgrounds and actions
• Killing superalgebras for Lorentzian four-manifolds
• $\mathcal{N}=2$ supersymmetric higher spin gauge theories and current multiplets in three dimensions
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Field theories with (2,0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace