Matrix Model as a Mirror of Chern-Simons Theory

Abstract

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators.

harvmac, 54 pages, 13 figures

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Cited by in corpus (141)

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• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Explicit examples of DIM constraints for network matrix models
• A-polynomial, B-model, and Quantization
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• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Exact results on ABJ theory and the refined topological string
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• Matrix models from operators and topological strings
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• Resumming the string perturbation series
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• ABJM Wilson Loops in Arbitrary Representations
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
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• The Partition Function of ABJ Theory
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• Non-Perturbative Topological Strings And Conformal Blocks
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• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
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• Two-Point Functions in ABJM Matrix Model
• Higher Rank ABJM Wilson Loops from Matrix Models
• On the exact R charge for N=2 CS theories
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Composite Representation Invariants and Unoriented Topological String Amplitudes
• ABCD of Beta Ensembles and Topological Strings
• 't Hooft Expansion of 1/2 BPS Wilson Loop
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• Towards U(N|M) knot invariant from ABJM theory
• Localization and Non-Renormalization in Chern-Simons Theory
• Phase Space Distribution of Riemann Zeros
• Penner Type Ensemble for Gauge Theories Revisited
• Linking loops in ABJM and refined theory
• $E_8$ spectral curves
• G_2 Holonomy, Mirror Symmetry and Phases of N=1 SYM
• Random matrix approach to three-dimensional QCD with a Chern-Simons term
• Five-dimensional gauge theories and the local B-model
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• BPS states, crystals and matrices
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