Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2

TL;DR

This paper develops self-dual N=2 supergravity theories in seven dimensions with G_2 holonomy, utilizing octonion structures to impose generalized self-duality constraints on superspace, and identifies two distinct formulations with different degrees of freedom.

Contribution

It introduces two novel self-dual N=2 supergravity models in 7D with G_2 holonomy, incorporating higher-order terms and octonion-based self-duality conditions.

Findings

Two self-dual supergravity theories with different spinor charge representations.

Explicit superspace constraints for self-duality in 7D supergravity.

Identification of on-shell degrees of freedom for each formulation.

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.