G(2) Holonomy Spaces from Invariant Three-Forms

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 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.

29 pages, LaTeX2e, corrected some typos

References in corpus (20)

• Chiral Four-Dimensional N=1 Supersymmetric Type IIA Orientifolds from Intersecting D6-Branes
• Three-Family Supersymmetric Standard-like Models from Intersecting Brane Worlds
• Chiral Fermions from Manifolds of $G_2$ Holonomy
• Gauge Theory at Large N and New G_2 Holonomy Metrics
• Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
• New Complete Non-compact Spin(7) Manifolds
• Orientifold, Geometric Transition and Large N Duality for SO/Sp Gauge Theories
• (Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry
• Mirror Symmetry and a $G_2$ Flop
• $G_2$ Manifolds, Mirror Symmetry and Geometric Engineering
• Cohomogeneity-one G2-structures
• M-theory Conifolds
• D-Branes, Holonomy and M-Theory
• Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and Spin(7) Holonomy
• Branes Wrapped on Coassociative Cycles
• On Spin(7) holonomy metric based on SU(3)/U(1): II
• Orientifolds and Slumps in G_2 and Spin(7) Metrics
• A New Fractional D2-brane, G_2 Holonomy and T-duality
• Duality and Confinement in N=1 Supersymmetric Theories from Geometric Transitions
• R^4 corrections to conifolds and G_2 holonomy metrics

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