文摘
英文文摘
Acknowledgements
Chapter1 Witten Conjecture And Its Generalizations
1.1 Introduction
1.2 Witten Conjecture
1.2.1 Intersection Theory of The Stable Moduli Space Mg,n
1.2.2 Descriptions For Witten Conjecture
1.3 Some Proofs of Witten Conjecture
1.3.1 Matrix Integral's Approach
1.3.2 Hurwitz Number's Approach
1.3.3 Weil-Peterson Volume's Approach
1.4 Some Generalizations of Witten Conjecture
1.4.1 Virasoro Conjecture
1.4.2 Witten's r-Spin Conjecture
1.5 Conclusion
Chapter2 Topological String Dualities From Physics
2.1 Introduction
2.2 Preliminaries in Topological Strings
2.2.1 From QFT to String Theory
2.2.2 N=(2,2) Supersymmetry
2.2.3 Topological String Partition Function
2.2.4 A-model and B-model Topological String Theory
2.2.5 Topological String and Type Ⅱ Superstring
2.3 Preliminaries in Related Mathematics
2.3.1 Calabi-Yau Manifold
2.3.2 Toric Geometry
2.3.3 Localization Formula
2.3.4 Quantum Group
2.4 T-Duality and Mirror Symmetry
2.4.1 T-Dulity
2.4.2 Mirror Principal
2.5 Large N Dualities
2.5.1 Gopakumar-Vafa Conjecture
2.5.2 Labastida-Mari(n)o-Ooguri-Vafa Conjecture
2.5.3 Mari(n)o-Vafa Conjecture
2.5.4 Topological Vertex
2.6 Conclusion
Bibliography