Geometry of all supersymmetric four-dimensional N=1 supergravity backgrounds

@inproceedings{Gran2008GeometryOA,
  title={Geometry of all supersymmetric four-dimensional N=1 supergravity backgrounds},
  author={Ulf Gran and J. B. Gutowski and George Papadopoulos},
  year={2008}
}
We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four supercharges, coupled to any number of vector and scalar multiplets in all cases. We find that backgrounds with N=1 supersymmetry admit a null, integrable, Killing vector field. There are two classes of N=2 backgrounds. The spacetime in the first class admits a parallel null vector field and so it is a pp-wave. The spacetime of the other class admits three Killing vector fields, and a vector field that commutes with… CONTINUE READING

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