# Geometry of all supersymmetric four-dimensional ${cal N}=1$ supergravity backgrounds - High Energy Physics - Theory

Geometry of all supersymmetric four-dimensional ${cal N}=1$ supergravity backgrounds - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with foursupercharges, coupled to any number of vector and scalar multiplets in allcases. We find that backgrounds with N=1 supersymmetry admit a null,integrable, Killing vector field. There are two classes of N=2 backgrounds. Thespacetime in the first class admits a parallel null vector field and so it is app-wave. The spacetime of the other class admits three Killing vector fields,and a vector field that commutes with the three Killing directions. Thesebackgrounds are of cohomogeneity one with homogenous sections either$\bR^{2,1}$ or $AdS 3$ and have an interpretation as domain walls. The N=3backgrounds are locally maximally supersymmetric. There are N=3 backgroundswhich arise as discrete identifications of maximally supersymmetric ones. Themaximally supersymmetric backgrounds are locally isometric to either$\bR^{3,1}$ or $AdS 4$.

Author: U. Gran, J. Gutowski, G. Papadopoulos

Source: https://arxiv.org/