Geometry of all supersymmetric four-dimensional ${\cal N}=1$ supergravity backgrounds

Details Geometry of all supersymmetric four-dimensional ${\cal N}=1$ supergravity backgrounds Geometry of all supersymmetric four-dimensional ${\cal N}=1$ supergravity backgrounds

2008-02-13

arxiv.org/abs/0802.1779v2

JHEP 0806:102,2008

Physics

High Energy Physics

High Energy Physics - Theory

15 pages; minor changes, references added, published version

Scientific paper

10.1088/1126-6708/2008/06/102

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 $AdS_4$.

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