Spin(7) holonomy manifold and Superconnection

Abstract

We discuss the higher dimensional generalization of gravitational instantons by using volume-preserving vector fields. We give special attention to the case of 8-dimensions and present a new construction of the Ricci flat metric with holonomy in Spin(7). An example of the metric is explicitly given. Further it is shown that our formulation has a natural interpretation in the Chern-Simons theory written by the language of superconnections.

12 pages

References in corpus (7)

• Hyper-Kahler manifolds and multiply-intersecting branes
• Chern-Simons and Twisted Supersymmetry in Higher Dimensions
• Supermembranes with fewer supersymmetries
• Ricci-Flat Branes
• Self-Duality in D <= 8-dimensional Euclidean Gravity
• Octonionic Gravitational Instantons
• Applications of the Ashtekar gravity to four dimensional hyperkähler geometry and Yang-Mills Instantons

Cited by in corpus (6)

• New Complete Non-compact Spin(7) Manifolds
• (Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry
• Coset Construction of $Spin(7),G_2$ Gravitational Instantons
• Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy
• On the Moyal deformation of Nahm Equations in seven dimensions
• Quillen superconnections and connections on supermanifolds