Abstract
We construct several new G 2 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 three-cycle 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 G 2 metric that is related in type IIA to the line bundle over S 2× S 2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G 2 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 G 2 holonomy metrics.
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