| Matrix Models, Chern-Simons Theory, and the Large N Expansion / I： |
| Matrix models / 1： |
| Basics of matrix models / 1.1： |
| Matrix model technology I: saddle-point analysis / 1.2： |
| Matrix model technology II: orthogonal polynomials / 1.3： |
| Chern-Simons theory and knot invariants / 2： |
| Chern-Simons theory: basic ingredients / 2.1： |
| Perturbative approach / 2.2： |
| Perturbative structure of the partition function / 2.2.1： |
| Group factors / 2.2.2： |
| Canonical quantization and surgery / 2.3： |
| Framing dependence / 2.4： |
| Results on Wilson loops and knot invariants / 2.5： |
| General properties / 2.5.1： |
| Torus knots / 2.5.2： |
| U([infinity]) representation theory / 2.6： |
| The 1/N expansion in Chern-Simons theory / 2.7： |
| Chern-Simons theory as a matrix model / 2.8： |
| Topological Strings / II： |
| Topological sigma models / 3： |
| The N = 2 supersymmetric sigma model / 3.1： |
| Topological twist / 3.2： |
| The topological type-A model / 3.3： |
| The topological type-B model / 3.4： |
| Topological strings / 4： |
| Coupling to gravity / 4.1： |
| Relation to compactifications of type II string theory / 4.2： |
| The type-A topological string / 4.3： |
| Mathematical description / 4.3.1： |
| Integrality properties and Gopakumar-Vafa invariants / 4.3.2： |
| Open topological strings / 4.4： |
| Type A model / 4.4.1： |
| Type-B model / 4.4.2： |
| Calabi-Yau geometries / 5： |
| Non-compact Calabi-Yau geometries: an introduction / 5.1： |
| Constructing toric Calabi-Yau manifolds / 5.2： |
| C[superscript 3] / 5.2.1： |
| The general case / 5.2.2： |
| The conifold transition / 5.3： |
| Examples of closed string amplitudes / 5.4： |
| The Topological String/Gauge Theory Correspondence / III： |
| String theory and gauge theory / 6： |
| String field theory and gauge theories / 7： |
| Open string field theory / 7.1： |
| Chern-Simons theory as an open string theory / 7.2： |
| Open topological strings on T* M / 7.2.1： |
| More general Calabi-Yau manifolds / 7.2.2： |
| Matrix model as an open string theory / 7.3： |
| Holomorphic Chern-Simons theory / 7.3.1： |
| Type B topological strings and matrix models / 7.3.2： |
| Open string amplitudes and multicut solutions / 7.3.3： |
| Geometric transitions / 8： |
| The conifold transition and the large N duality / 8.1： |
| Incorporating Wilson loops / 8.2： |
| Geometric transitions for more general toric manifolds / 8.3： |
| Matrix models and geometric transitions / 8.4： |
| The topological vertex / 9： |
| Framing of topological open string amplitudes / 9.1： |
| Definition of the topological vertex / 9.2： |
| Gluing rules / 9.3： |
| Derivation of the topological vertex / 9.4： |
| Useful formulae for the vertex / 9.5： |
| Some applications / 9.6： |
| Further properties of the topological vertex / 9.7： |
| Applications of the topological string/gauge theory correspondence / 10： |
| Applications to knot invariants / 10.1： |
| Applications to N = 2 supersymmetric gauge theory / 10.2： |
| Symmetric polynomials / A： |
| References |
| Index |
| Matrix Models, Chern-Simons Theory, and the Large N Expansion / I： |
| Matrix models / 1： |
| Basics of matrix models / 1.1： |
図書
