Mirror Symmetry and a $G_2$ Flop

Abstract

By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a $G_2$ flop in M-theory relevant for large $N$ dualities in $\mathcal{N}=1$ supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on corresponding $G_2$ manifolds for all A-D-E cases. This provides an effective method for geometric engineering of $\mathcal{N}=1$ gauge theories for which mirror symmetry gives exact information about vacuum geometry. We also find a number of interesting dual descriptions.

Identification of parameters as well as the computation of the superpotential is extended to all A-D-E cases. Additional references are also included

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Cited by in corpus (38)

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• On N=1 Mirror Symmetry for Open Type II Strings
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• Phase transitions, double-scaling limit, and topological strings
• Supersymmetric M3-branes and G_2 Manifolds
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• Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and Spin(7) Holonomy
• Branes Wrapped on Coassociative Cycles
• Superconformal Field Theories for Compact G_2 Manifolds
• Baryons, Boundaries and Matrix Models
• Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds
• Supersymmetric Configurations, Geometric Transitions and New Non-Kahler Manifolds
• Summing up Open String Instantons and N=1 String Amplitudes
• Non-perturbative orientifold transitions at the conifold
• Supersymmetry, G-flux and Spin(7) manifolds
• A New Fractional D2-brane, G_2 Holonomy and T-duality
• D-brane probes on G2 Orbifolds
• On the equivalence of N=1 brane worlds and geometric singularities with flux
• F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry
• New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities
• Comments on M Theory Dynamics on G2 Holonomy Manifolds
• Intersection theory of coassociative submanifolds in G_(2)-manifolds and Seiberg-Witten invariants
• G_2 Holonomy, Mirror Symmetry and Phases of N=1 SYM
• Harmonic Higgs Bundles and Coassociative ALE Fibrations
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• Geometric Transitions, del Pezzo Surfaces and Open String Instantons
• Instantons in G2 manifolds from J-holomorphic curves in coassociative submanifolds
• Computations on B-model geometric transitions
• Superpotential of the M-theory conifold and type IIA string theory
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
• Manifolds with reduced holonomy in superstring theories
• Thin instantons in G_2-manifolds and Seiberg-Witten invariants
• Geometric Transitions and Open String Instantons