Towards ${\cal N}=8$ Supergravity in ${\cal N}=1$ Superspace

Abstract

We study the possibility of constructing maximally supersymmetric supergravity in ${\cal N}=1$ superspace. We dimensionally reduce the eleven dimensional supersymmetry transformations, and decouple these transformations using the residual $G_2$ symmetry of the theory. This allows us to find the ${\cal N}=1$ superfields relevant to this theory. Among our results, we find a description of a self-dual superfield involving a spin 1 and a spin 3/2 field which does not seem to have been discussed previously in the literature.