Coset Construction of $Spin(7), G_2$ Gravitational Instantons

Y. Konishi; M. Naka

doi:10.1088/0264-9381/18/24/314

paper

Coset Construction of $S p in (7), G_{2}$ Gravitational Instantons

arXiv:hep-th/0104208 · doi:10.1088/0264-9381/18/24/314

Abstract

We study Ricci-flat metrics on non-compact manifolds with the exceptional holonomy $S p in (7), G_{2}$ . We concentrate on the metrics which are defined on $R \times G / H$ . If the homogeneous coset spaces $G / H$ have weak $G_{2}$ , SU(3) holonomy, the manifold $R \times G / H$ may have $S p in (7), G_{2}$ holonomy metrics. Using the formulation with vector fields, we investigate the metrics with $S p in (7)$ holonomy on $R \times S p (2) / S p (1), R \times S U (3) / U (1)$ . We have found the explicit volume-preserving vector fields on these manifold using the elementary coordinate parameterization. This construction is essentially dual to solving the generalized self-duality condition for spin connections. We present most general differential equations for each coset. Then, we develop the similar formulation in order to calculate metrics with $G_{2}$ holonomy

29 pages, no figure; (v2) Errors are corrected ; (v3) Some explanations are added. More general differential equations for SU(3)/U(1) coset are given

Coset Construction of $S p in (7), G_{2}$ Gravitational Instantons

Abstract

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Cited by in corpus (18)

Coset Construction of Spin(7),G2​ Gravitational Instantons

Abstract

References in corpus (6)

Cited by in corpus (18)

Coset Construction of $S p in (7), G_{2}$ Gravitational Instantons