G2 holonomy spaces from invariant three-forms

Abstract 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 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 G2 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 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.