Large N Duality, Lens Spaces and the Chern-Simons Matrix Model

Abstract

We demonsrate that the spectral curve of the matrix model for Chern-Simons theory on the Lens space S^{3}/\ZZ_p is precisely the Riemann surface which appears in the mirror to the blownup, orbifolded conifold. This provides the first check of the $A$-model large $N$ duality for T^{*}(S^{3}/\ZZ_p), p>2.

12 pages, 2 figures

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• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Geometric Engineering of Quantum Field Theories
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
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• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
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• Matrix Model as a Mirror of Chern-Simons Theory
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Cited by in corpus (22)

• Exact Results in ABJM Theory from Topological Strings
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• A holomorphic and background independent partition function for matrix models and topological strings
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Seiberg-Witten theory and matrix models
• Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Large N duality beyond the genus expansion
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• Exact results for topological strings on resolved Y(p,q) singularities
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Matrix model from N = 2 orbifold partition function
• The Volume Conjecture and Topological Strings
• Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
• Bubbling Calabi-Yau geometry from matrix models
• Intersecting Defects and Supergroup Gauge Theory
• Trivializing and Orbifolding the Conifold's Base
• Introduction to the Gopakumar-Vafa Large N Duality
• Higher Rank ABJM Wilson Loops from Matrix Models
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models