Mirror Manifolds And Topological Field Theory

Abstract

These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.

35 pp

References in corpus (1)

• Topological Field Theory and Rational Curves

Cited by in corpus (251)

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• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Criteria for Conformal Invariance of (0,2) Models
• Chern-Simons Theory and Topological Strings
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• Les Houches lectures on matrix models and topological strings
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• Superpotentials and Membrane Instantons
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• On the structure of open-closed topological field theory in two dimensions
• Measuring Small Distances in N=2 Sigma Models
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• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
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• Topological Orbifold Models and Quantum Cohomology Rings
• Derived Categories and Zero-Brane Stability
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• Anomalies, Conformal Manifolds, and Spheres
• D-branes, open string vertex operators, and Ext groups
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• Computation of Superpotentials for D-Branes
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• Chern-Simons Gauge Theory As A String Theory
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• All solutions of the localization equations for N=2 quantum black hole entropy
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• New Instanton Effects In Supersymmetric QCD
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• Enhanced D-Brane Categories from String Field Theory
• The Hitchin functionals and the topological B-model at one loop
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• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
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• Lectures on Mirror Symmetry and Topological String Theory
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• Jacobi sigma models
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• Holomorphic Supercurves and Supersymmetric Sigma Models
• Anomaly cancellation in the topological string
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• Graded D-branes and skew-categories
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• Comments on chiral algebras and $\Omega$-deformations
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• Mirror symmetry for quasi-smooth Calabi-Yau hypersurfaces in weighted projective spaces
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• Topological Sigma Models On Supermanifolds
• Taming open/closed string duality with a Losev trick
• The Affine Hidden Symmetry and Integrability of Type IIB Superstring in $Ad{S}_5\times S^5$
• Entanglement entropy and edge modes in topological string theory: I
• Topological Correlators in Landau-Ginzburg Models with Boundaries
• Singular BPS boundary conditions in $\mathcal{N}=(2,2)$ supersymmetric gauge theories
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• Notes on correlation functions in (0,2) theories
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• Topological and dynamical aspects of Jacobi sigma models
• Mirror Symmetry and Discriminants
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• Towards A Topological G_2 String
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• Equivariant Cohomology Of The Chiral de Rham Complex And The Half-Twisted Gauged Sigma Model
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• Topological D-branes from Descent
• Kähler Potential of Moduli Space in Large Radius Region of Calabi-Yau Manifold
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• Axion decay constants at special points in type II string theory
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• BRST Approach to Hamiltonian Systems
• On deformation theory of quantum vertex algebras
• General Mirror Pairs for Gauged Linear Sigma Models
• Identification of Two Frobenius Manifolds In Mirror Symmetry
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• Generalized Topological Sigma Model
• Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties
• Supersymmetric Gauge Theories from String Theory
• Topological Sigma B Model in 4-Dimensions
• Open/Closed Topological CP1 Sigma Model Revisited
• Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras
• $N=1$ fermionic D3-branes in RNS formulation I. $C^{\infty }$-Algebrogeometric foundations of $d=4$, $N=1$ supersymmetry, SUSY-rep compatible hybrid connections, and $\hat{D}$-chiral maps from a $d=4$ $N=1$ Azumaya/matrix superspace
• On the Magnetic Current Density in the Maxwell Equations Based on the Noether Theorem
• B-strings on non-Kählerian manifolds
• Coisotropic Branes in Toric Calabi-Yau 3-folds
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• The Half-Twisted Orbifold Sigma Model and the Chiral de Rham Complex
• N=2 String Geometry and the Heavenly Equations
• Study of the OSV Conjecture for 4D N=2 Extremal Black Holes in Type IIB String Theory
• D-branes, actions effectives et symétrie miroir
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• B-branes and the Derived Category
• Gromov-Witten Theory and Threshold Corrections
• Algebra of Kodaira-Spencer Gravity and Deformation of Calabi-Yau Manifold
• Hypersurfaces and generalized deformations
• Thickening Calabi-Yau moduli spaces
• Some notes on string theory
• Topics in Open Topological Strings
• An alternative BRST operator for topological Landau-Ginzburg models
• Geometrical Aspect of Topologically Twisted 2-Dimensional Conformal Superalgebra
• A Gamma Class Formula for Open Gromov-Witten Calculations
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• Genus One Partition Function of the Calabi-Yau d-Fold embedded in $C{P}^{d+1}$
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