Spin(7) holonomy manifold and Superconnection
Yukinori Yasui, Takayoshi Ootsuka
TL;DR
This paper introduces a new construction of Ricci-flat metrics with Spin(7) holonomy in eight dimensions, connecting higher-dimensional gravitational instantons with superconnections and Chern-Simons theory.
Contribution
It presents a novel method for constructing Spin(7) holonomy manifolds using volume-preserving vector fields and superconnections, with explicit examples and theoretical insights.
Findings
Explicit Ricci-flat metric with Spin(7) holonomy provided
Formulation linked to Chern-Simons theory and superconnections
New approach to higher-dimensional gravitational instantons
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.
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