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

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.

14 pages, no figures. Some missing references, typos and grammatical errors have been corrected with other relatively minor improvements

References in corpus (5)

• G(2) Holonomy Spaces from Invariant Three-Forms
• M-theory compactifications on certain `toric' cones of $G_2$ holonomy
• Integrable reductions of Spin(7) and G_2 invariant self-dual Yang-Mills equations and gravity
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• Eight-Dimensional Topological Gravity and its Correspondence with Supergravity

Cited by in corpus (6)

• Towards an Ashtekar formalism in eight dimensions
• Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8
• Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2
• Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri
• Towards an Ashtekar Formalism in Twelve Dimensions
• Chiral gravity in higher dimensions