Self-Dual N=(1,0) Supergravity in Eight Dimensions with Reduced Holonomy Spin(7)

TL;DR

This paper constructs a chiral N=(1,0) self-dual supergravity theory in eight dimensions with Spin(7) holonomy, incorporating higher-order interactions and ensuring compatibility of supersymmetry with self-duality and reduced holonomy.

Contribution

It develops the first explicit formulation of self-dual supergravity in eight dimensions with Spin(7) holonomy, including all higher-order interactions in a consistent supersymmetric framework.

Findings

Established non-chiral N=(1,1) supergravity with SO(8) holonomy.

Formulated self-dual supergravity with Spin(7) holonomy in a closed form.

Ensured compatibility of supersymmetry, self-duality, and reduced holonomy.

Abstract

We construct chiral N=(1,0) self-dual supergravity in Euclidean eight-dimensions with reduced holonomy Spin(7), including all the higher-order interactions in a closed form. We first establish the non-chiral N=(1,1) superspace supergravity in eight-dimensions with SO(8) holonomy without self-duality, as the foundation of the formulation. In order to make the whole computation simple, and the generalized self-duality compatible with supersymmetry, we adopt a particular set of superspace constraints similar to the one originally developed in ten-dimensional superspace. The intrinsic properties of octonionic structure constants make local supersymmetry, generalized self-duality condition, and reduced holonomy Spin(7) all consistent with each other.