G(2) Holonomy Spaces from Invariant Three-Forms

Details G(2) Holonomy Spaces from Invariant Three-Forms G(2) Holonomy Spaces from Invariant Three-Forms

2001-12-13

arxiv.org/abs/hep-th/0112113v2

Nucl.Phys. B629 (2002) 393-416

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, LaTeX2e, corrected some typos

Scientific paper

10.1016/S0550-3213(02)00146-3

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 x 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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