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

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 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-normalizable solution that deforms the asymptotic radius of the M theory circle. e-mail: [email protected] e-mail: [email protected]