دانلود کتاب Chern-Simons Theory, Matrix Models And Topological Strings

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PREFACE......Page 8
ACKNOWLEDGEMENTS......Page 11
Contents......Page 12
I: MATRIX MODELS, CHERN–SIMONS THEORY, AND THE LARGE N EXPANSION......Page 14
1.1 Basics of matrix models......Page 16
1.2 Matrix model technology I: saddle-point analysis......Page 24
1.3 Matrix model technology II: orthogonal polynomials......Page 31
2.1 Chern–Simons theory: basic ingredients......Page 38
2.2 Perturbative approach......Page 42
2.3 Canonical quantization and surgery......Page 49
2.4 Framing dependence......Page 57
2.5 Results on Wilson loops and knot invariants......Page 59
2.6 U(∞) representation theory......Page 64
2.7 The 1/N expansion in Chern–Simons theory......Page 72
2.8 Chern–Simons theory as a matrix model......Page 75
II: TOPOLOGICAL STRINGS......Page 82
3.1 The N = 2 supersymmetric sigma model......Page 84
3.2 Topological twist......Page 86
3.3 The topological type-A model......Page 91
3.4 The topological type-B model......Page 96
4.1 Coupling to gravity......Page 100
4.2 Relation to compactifications of type II string theory......Page 101
4.3 The type-A topological string......Page 102
4.4 Open topological strings......Page 110
5.1 Non-compact Calabi–Yau geometries: an introduction......Page 120
5.2 Constructing toric Calabi–Yau manifolds......Page 122
5.3 The conifold transition......Page 128
5.4 Examples of closed string amplitudes......Page 131
III: THE TOPOLOGICAL STRING/GAUGE THEORY CORRESPONDENCE......Page 134
6 String theory and gauge theory......Page 136
7.1 Open string field theory......Page 140
7.2 Chern–Simons theory as an open string theory......Page 141
7.3 Matrix model as an open string theory......Page 146
8.1 The conifold transition and the large N duality......Page 156
8.2 Incorporating Wilson loops......Page 157
8.3 Geometric transitions for more general toric manifolds......Page 161
8.4 Matrix models and geometric transitions......Page 166
9.1 Framing of topological open string amplitudes......Page 170
9.2 Definition of the topological vertex......Page 171
9.3 Gluing rules......Page 173
9.4 Derivation of the topological vertex......Page 175
9.5 Useful formulae for the vertex......Page 179
9.6 Some applications......Page 181
9.7 Further properties of the topological vertex......Page 186
10.1 Applications to knot invariants......Page 190
10.2 Applications to N = 2 supersymmetric gauge theory......Page 193
A: Symmetric polynomials......Page 198
References......Page 200
Index......Page 210