On the Global Structure of Some Natural Fibrations of Joyce Manifolds
Abstract
The study of fibrations of the target manifolds of string/M/Ftheories has provided many insights to the dualities among these theories or even as a tool to build up dualities since the work of Strominger, Yau, and Zaslow on the CalabiYau case. For Mtheory compactified on a Joyce manifold $M^7$, the fact that $M^7$ is constructed via a generalized Kummer construction on a 7torus ${\smallBbb T}^7$ with a torsionfree $G_2$structure $\phi$ suggests that there are natural fibrations of $M^7$ by ${\smallBbb T}^3$, ${\smallBbb T}^4$, and K3 surfaces in a way governed by $\phi$. The local picture of some of these fibrations and their roles in dualities between string/Mtheory have been studied intensively in the work of Acharya. In this present work, we explain how one can understand their global and topological details in terms of bundles over orbifolds. After the essential background is provided in Sec. 1, we give general discussions in Sec. 2 about these fibrations, their generic and exceptional fibers, their monodromy, and the base orbifolds. Based on these, one obtains a 5steproutine to understand the fibrations, which we illustrate by examples in Sec. 3. In Sec. 4, we turn to another kind of fibrations for Joyce manifolds, namely the fibrations by the CalabiYau threefolds constructed by Borcea and Voisin. All these fibrations arise freely and naturally from the work of Joyce. Understanding how the global structure of these fibrations may play roles in string/Mtheory duality is one of the major issues for further pursuit.
 Publication:

arXiv eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.hepth/9809007
 arXiv:
 arXiv:hepth/9809007
 Bibcode:
 1998hep.th....9007L
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology
 EPrint:
 36 pages