Holonomy Spaces from Invariant Three - Forms


We construct several new G2 holonomy metrics that play an important role in recent studies of geometrical transitions in compactifications of M-theory to four dimensions. In type IIA string theory these metrics correspond to D6 branes wrapped on the threecycle of the deformed conifold and the resolved conifold with two-form RR flux on the blown-up two-sphere, which are related by a conifold transition. We also study a G2 metric that is related in type IIA to the line bundle over S×S2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G2 structures in terms of three-forms which are closed and co-closed. Besides being an elegant formalism this turns out to be a practical tool to construct G2 holonomy metrics.

Cite this paper

@inproceedings{Brandhuber2008HolonomySF, title={Holonomy Spaces from Invariant Three - Forms}, author={Andreas Brandhuber}, year={2008} }