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arXiv · 0802.1779

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

U. Gran·J. Gutowski·G. Papadopoulos
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Abstract

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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U. Gran, J. Gutowski, G. Papadopoulos. 2008-06-17. Geometry of all supersymmetric four-dimensional ${\cal N}=1$ supergravity backgrounds. https://doi.org/10.1088/1126-6708%2F2008%2F06%2F102

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