Harmonic Forms and Deformation of ALC metrics with Spin(7) holonomy
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.
Cite
@article{arxiv.hep-th/0208139,
title = {Harmonic Forms and Deformation of ALC metrics with Spin(7) holonomy},
author = {Hiroaki Kanno and Yukinori Yasui},
journal= {arXiv preprint arXiv:hep-th/0208139},
year = {2010}
}
Comments
33 pages, no figure, minor corrections, reference added