Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2

Abstract

We present self-dual N=2 supergravity in superspace for Euclidean seven dimensions with the reduced holonomy G_2 \subset SO(7), including all higher-order terms. As its foundation, we first establish N=2 supergravity without self-duality in Euclidean seven dimensions. We next show how the generalized self-duality in terms of octonion structure constants can be consistently imposed on the superspace constraints. We found two self-dual N=2 supergravity theories possible in 7D, depending on the representations of the two spinor charges of N=2. The first formulation has both of the two spinor charges in the {\bf 7} of G_2 with 24 + 24 on-shell degrees of freedom. The second formulation has both charges in the {\bf 1} of G_2 with 16 + 16 on-shell degrees of freedom.