$G_2$ Manifolds, Mirror Symmetry and Geometric Engineering

Details $G_2$ Manifolds, Mirror Symmetry and Geometric Engineering $G_2$ Manifolds, Mirror Symmetry and Geometric Engineering

2001-10-18

arxiv.org/abs/hep-th/0110171v1

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, harvmac

Scientific paper

We construct Calabi-Yau geometries with wrapped D6 branes which realize ${\cal N}=1$ supersymmetric $A_r$ quiver theories, and study the corresponding geometric transitions. This also yields new large $N$ dualities for topological strings generalizing topological strings/large $N$ Chern-Simons duality. Lifting up to M-theory yields smooth quantum geometric transitions without branes or fluxes, in the context of $G_2$ holonomy manifolds. In addition we construct a linear sigma model realization which is relevant for the worldsheet theory of superstrings propagating in local manifolds with $G_2$ holonomy, and obtain mirror geometries for this class of supersymmetric sigma models.

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