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Harmonic Forms and Deformation of ALC metrics with Spin(7) holonomy

Hiroaki Kanno·Yukinori Yasui
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Abstract

Asymptotically locally conical (ALC) metric of exceptional holonomy has an asymptotic circle bundle structure that accommodates the M theory circle in type IIA reduction. Taking Spin(7) metrics of cohomogeneity one as explicit examples, we investigate deformations of ALC metrics, in particular that change the asymptotic S^1 radius related to the type IIA string coupling constant. When the canonical four form of Spin(7) holonomy is taken to be anti-self-dual, the deformations of Spin(7) metric are related to the harmonic self-dual four forms, which are given by solutions to a system of first order differential equations, due to the metric ansatz of cohomogeneity one. We identify the L^2-normalizable solution that deforms the asymptotic radius of the M theory circle.

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Hiroaki Kanno, Yukinori Yasui. 2002-08-28. Harmonic Forms and Deformation of ALC metrics with Spin(7) holonomy. https://doi.org/10.1016/s0550-3213(02)01073-8

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