Lectures on Mirror Symmetry and Topological String Theory

Abstract

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observables are only the elements of the chiral ring. When coupled to gravity, this leads to topological string theory. The identification of the topological string A- and B-models by mirror symmetry leads to surprising connections in mathematics and provides tools for exact computations as well as new insights in physics. A recursive construction of the higher genus amplitudes of topological string theory expressed as polynomials is reviewed.

44 pages, 1 figure

References in corpus (33)

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• Phases of $N=2$ Theories In Two Dimensions
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Geometric Engineering of Quantum Field Theories
• Black Hole Attractors and the Topological String
• Mirror Manifolds And Topological Field Theory
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• Quantum Background Independence In String Theory
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• Direct Integration of the Topological String
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• Measuring Small Distances in N=2 Sigma Models
• GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
• Integrability of the holomorphic anomaly equations
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• Differential Equations for Periods and Flat Coordinates in Two Dimensionsional Topological Matter Theories
• Picard-Fuchs Equations and Special Geometry
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Topological wave functions and heat equations
• A mini-course on topological strings
• The String Partition Function for QCD on the Torus
• Global Properties of Topological String Amplitudes and Orbifold Invariants
• Flat Holomorphic Connections and Picard-Fuchs Identities From $N=2$ Supergravity
• Topological strings and their physical applications
• The Moduli Space of N = 2 Superconformal Field Theories
• Topological Amplitudes and Physical Couplings in String Theory
• GKZ Hypergeometric Systems and Applications to Mirror Symmetry
• Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
• Mirror Symmetry of Calabi-Yau Manifolds and Flat Coordinates

Cited by in corpus (6)

• D-brane central charge and Landau-Ginzburg orbifolds
• Universality of the topological string at large radius and NS-brane resurgence
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Gauss-Manin connection in disguise: Genus two curves
• Algebraic structure of $t{t}^{\ast }$ equations for Calabi-Yau sigma models
• Lectures on BCOV holomorphic anomaly equations