Symmetries of curved superspace

Abstract

The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N=1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgrounds associated with any supergravity theory formulated in superspace. In particular, it has already been used to construct rigid supersymmetric field theories in 5D N=1, 4D N=2 and 3D (p,q) anti-de Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in off-shell 4D N=1 supergravity theories using component field considerations. Here we demonstrate how to read off the key results of these recent publications from the more general superspace approach developed in the 1990s. We also present a universal superspace setting to construct supersymmetric backgrounds, which is applicable to any of the known off-shell formulations for N=1 supergravity. This approach is based on the realizations of the new minimal and non-minimal supergravity theories as super-Weyl invariant couplings of the old minimal supergravity to certain conformal compensators.

21 pages; V2: references and comments added, published version

References in corpus (6)

• Exploring Curved Superspace
• 4D N = 2 Supergravity and Projective Superspace
• Exploring Curved Superspace (II)
• Three-dimensional (p,q) AdS superspaces and matter couplings
• Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics
• Nonlinear sigma models with AdS supersymmetry in three dimensions

Cited by in corpus (20)

• Extended Supersymmetry on Curved Spaces
• Supersymmetry on curved spaces and superconformal anomalies
• Supercurrent anomalies in 4d SCFTs
• Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography
• Three-dimensional N=2 supergravity theories: From superspace to components
• Higher spin supercurrents in anti-de Sitter space
• Nilpotent chiral superfield in N=2 supergravity and partial rigid supersymmetry breaking
• Symmetries of curved superspace in five dimensions
• Rigid 4D N=2 supersymmetric backgrounds and actions
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Symmetries of supergravity backgrounds and supersymmetric field theory
• Killing superalgebras for Lorentzian four-manifolds
• Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories
• Supersymmetry anomalies in new minimal supergravity
• Imaginary supergravity or Virial supergravity?
• Maximally supersymmetric solutions of $R^2$ supergravity
• Minimal $\mathcal{N}=4$ topologically massive supergravity
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
• On FLRW reductions of N=1 supergravity