# Geometry of all supersymmetric four-dimensional N=1 supergravity backgrounds Journal article, 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 the three Killing directions. These backgrounds are of cohomogeneity one with homogenous sections either $\bR^{2,1}$ or $AdS_3$ and have an interpretation as domain walls. The N=3 backgrounds are locally maximally supersymmetric. There are N=3 backgrounds which arise as discrete identifications of maximally supersymmetric ones. The maximally supersymmetric backgrounds are locally isometric to either $\bR^{3,1}$ or $AdS_4$.

## Author

### Ulf Gran

Chalmers, Applied Physics, Mathematical Physics

### Jan Gutowski

University of Cambridge

King's College London

#### Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 06 6 102-

### Subject Categories

Subatomic Physics

### DOI

10.1088/1126-6708/2008/06/102