$G_2$ Manifolds, Mirror Symmetry and Geometric Engineering

Abstract

We construct Calabi-Yau geometries with wrapped D6 branes which realize $\mathcal{N}=1$ 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.

35 pages, harvmac

References in corpus (22)

• Phases of $N=2$ Theories In Two Dimensions
• Superstrings and Topological Strings at Large N
• D-Branes And Mirror Symmetry
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
• Disk Instantons, Mirror Symmetry and the Duality Web
• An M-theory Flop as a Large N Duality
• Open string instantons and superpotentials
• Chiral Fermions from Manifolds of $G_2$ Holonomy
• Gauge Theory at Large N and New G_2 Holonomy Metrics
• Superpotentials and Membrane Instantons
• On Realising N=1 Super Yang-Mills in M theory
• Geometric Transitions and N=1 Quiver Theories
• Geometry of N=1 Dualities in Four Dimensions
• Geometric Transition, Large N Dualities and MQCD Dynamics
• Orientifold, Geometric Transition and Large N Duality for SO/Sp Gauge Theories
• M-theory on Manifolds of G_2 Holonomy and Type IIA Orientifolds
• Mirror Symmetry and a $G_2$ Flop
• Supersymmetric M3-branes and G_2 Manifolds
• On Mirror Symmetry for Manifolds of Exceptional Holonomy
• Disc Instantons in Linear Sigma Models
• Anomaly Cancellation On Manifolds Of G_2 Holonomy

Cited by in corpus (34)

• Vortex Counting and Lagrangian 3-manifolds
• Chern-Simons Theory and Topological Strings
• M theory and Singularities of Exceptional Holonomy Manifolds
• Knot Homology from Refined Chern-Simons Theory
• A Stringy Origin of M2 Brane Chern-Simons Theories
• On N=1 Mirror Symmetry for Open Type II Strings
• G(2) Holonomy Spaces from Invariant Three-Forms
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• Gauge Theories at Resolved and Deformed Singularities using Dimers
• Topological Open String Amplitudes On Orientifolds
• D-Brane Probes of Special Holonomy Manifolds
• Gauge/Liouville Triality
• Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and Spin(7) Holonomy
• Superconformal Field Theories for Compact G_2 Manifolds
• The Geometry of D-Brane Superpotentials
• Baryons, Boundaries and Matrix Models
• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds
• D-branes as a Bubbling Calabi-Yau
• Summing up Open String Instantons and N=1 String Amplitudes
• Supersymmetry, G-flux and Spin(7) manifolds
• D-brane probes on G2 Orbifolds
• The Topological G2 String
• D-Brane Probes of G_2 Holonomy Manifolds
• On the equivalence of N=1 brane worlds and geometric singularities with flux
• On Type II Strings in Two Dimensions
• Comments on M Theory Dynamics on G2 Holonomy Manifolds
• Toric Geometry and String Theory
• Toric Geometry and String Theory Descriptions of Qudit Systems
• D Branes and Phases on String Worldsheet
• Chern-Simons matrix model for local conifold
• Geometric Transitions and Mixed Hodge Structures
• New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals
• A Large N Type IIB Duality via a Spin(7) Geometric Transition as an F-theory Flop