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Mirror Symmetry Book

Mirror Symmetry
Mirror Symmetry, Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomor, Mirror Symmetry has a rating of 4 stars
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Mirror Symmetry, Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomor, Mirror Symmetry
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  • Mirror Symmetry
  • Written by author Kentaro Hori
  • Published by American Mathematical Society, August 2003
  • Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomor
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Preface
Introduction
Pt. 1Mathematical Preliminaries1
Ch. 1Differential Geometry3
Ch. 2Algebraic Geometry25
Ch. 3Differential and Algebraic Topology41
Ch. 4Equivariant Cohomology and Fixed-Point Theorems57
Ch. 5Complex and Kahler Geometry67
Ch. 6Calabi Yan Manifolds and Their Moduli77
Ch. 7Toric Geometry for String Theory101
Pt. 2Physics Preliminaries143
Ch. 8What Is a QFT?145
Ch. 9QFT in d = 0151
Ch. 10QFT in Dimension 1: Quantum Mechanics169
Ch. 11Free Quantum Field Theories in 1 + 1 Dimensions237
Ch. 12N = (2,2) Supersymmetry271
Ch. 13Non-linear Sigma Models and Landau-Ginzburg Models291
Ch. 14Renormalization Group Flow313
Ch. 15Linear Sigma Models339
Ch. 16Chiral Rings and Topological Field Theory397
Ch. 17Chiral Rings and the Geometry of the Vacuum Bundle423
Ch. 18BPS Solitons N = 2 Landau - Ginzburg Theories435
Ch. 19D-branes449
Pt. 3Mirror Symmetry: Physics Proof461
Ch. 20Proof of Mirror Symmetry463
Pt. 4Mirror Symmetry: Mathematics Proof481
Ch. 21Introduction and Overview483
Ch. 22Complex Curves (Non-singular and Nodal)487
Ch. 23Moduli Spaces of Curves493
Ch. 24Moduli Spaces [actual symbol not reproducible] of Stable Maps501
Ch. 25Cohomology Classes on [actual symbol not reproducible] and [actual symbol not reproducible]509
Ch. 26The Virtual Fundamental Class, Gromov-Witten Invariants, and Descendant Invariants519
Ch. 27Localization on the Moduli Space of Maps535
Ch. 28The Fundamental Solution of the Quantum Differential Equation553
Ch. 29The Mirror Conjecture for Hypersurfaces I: The Fano Case559
Ch. 30The Mirror Conjecture for Hypersurfaces II: The Calabi-Yau Case571
Pt. 5Advanced Topics583
Ch. 31Topological Strings585
Ch. 32Topological Strings and Target Space Physics599
Ch. 33Mathematical Formulation of Gopakumar-Vafa Invariants615
Ch. 34Multiple Covers, Integrality, and Gopakumar - Vafa Invariants635
Ch. 35Mirror Symmetry at Higher Genus645
Ch. 36Some Applications of Mirror Symmetry677
Ch. 37Aspects of Mirror Symmetry and D-branes691
Ch. 38More on the Mathematics of D-branes: Bundles, Derived Categories, and Lagrangians729
Ch. 39Boundary N = 2 Theories765
Ch. 40References889
Bibliography905
Index921


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