10 Type Ⅰ and type Ⅱ superstrings 1
10.1 The superconformal algebra 1
10.2 Ramond and Neveu-Schwarz sectors 5
10.3 Vertex operators and bosonization 10
10.4 The superconformal ghosts 15
10.5 Physical states 20
10.6 Superstring theories in ten dimensions 25
10.7 Modular invariance 31
10.8 Divergences of type Ⅰ theory 37
Exercises 43
11 The heterotic string 45
11.1 World-sheet supersymmetries 45
11.2 The SO(32) and E8×E8 heterotic strings 49
11.3 Other ten-dimensional heterotic strings 55
11.4 A little Lie algebra 59
11.5 Current algebras 66
11.6 The bosonic construction and toroidal compactification 73
Exercises 82
12 Superstring interactions 84
12.1 Low energy supergravity 84
12.2 Anomalies 94
12.3 Superspace and superfields 103
12.4 Tree-level amplitudes 110
12.5 General amplitudes 118
12.6 One-loop amplitudes 126
Exercises 134
13 D-branes 136
13.1 T-duality of type Ⅱ strings 136
13.2 T-duality of type Ⅰ strings 138
13.3 The D-brane charge and action 146
13.4 D-brane interactions:statics 152
13.5 D-brane interactions:dynamics 158
13.6 D-brane interactions:bound states 164
Exercises 175
14 Strings at strong coupling 178
14.1 Type ⅡB string and SL(2,Z) duality 179
14.2 U-duality 187
14.3 SO(32) type Ⅰ-heterotic duality 190
14.4 Type ⅡA string and M-theory 198
14.5 The E8×E8 heterotic string 205
14.6 What is string theory? 208
14.7 Is M for matrix? 211
14.8 Black hole quantum mechanics 219
Exercises 226
15 Advanced CFT 228
15.1 Representations of the Virasoro algebra 228
15.2 The conformal bootstrap 233
15.3 Minimal models 236
15.4 Current algebras 243
15.5 Coset models 250
15.6 Representations of the N=1 superconformal algebra 254
15.7 Rational CFT 255
15.8 Renormalization group flows 259
15.9 Statistical mechanics 266
Exercises 271
16 Orbifolds 274
16.1 Orbifolds of the heterotic string 275
16.2 Spacetime supersymmetry 281
16.3 Examples 283
16.4 Low energy field theory 292
Exercises 300
17 Calabi-Yau compactification 302
17.1 Conditions for N=1 supersymmetry 302
17.2 Calabi-Yau manifolds 305
17.3 Massless spectrum 312
17.4 Low energy field theory 315
17.5 Higher corrections 321
17.6 Generalizations 324
18 Physics in four dimensions 327
18.1 Continuous and discrete symmetries 327
18.2 Gauge symmetries 335
18.3 Mass scales 343
18.4 More on unification 351
18.5 Conditions for spacetime supersymmetry 356
18.6 Low energy actions 359
18.7 Supersymmetry breaking in perturbation theory 362
18.8 Supersymmetry beyond perturbation theory 366
Exercises 373
19 Advanced topics 375
19.1 The N=2 superconformal algebra 375
19.2 Type Ⅱ strings on Calabi-Yau manifolds 379
19.3 Heterotic string theories with(2,2)SCFT 386
19.4 N=2 minimal models 390
19.5 Gepner models 394
19.6 Mirror symmetry and applications 402
19.7 The conifold 409
19.8 String theories on K3 415
19.9 String duality below ten dimensions 421
19.10 Conclusion 429
Exercises 429
Appendix B:Spinors and SUSY in various dimensions 430
B.1 Spinors in various dimensions 430
B.2 Introduction to supersymmetry:d=4 439
B.3 Supersymmetry in d=2 449
B.4 Differential forms and generalized gauge fields 450
B.5 Thirty-two supersymmetries 452
B.6 Sixteen supersymmetries 457
B.7 Eight supersymmetries 461
Exercises 466
References 467
Glossary 488
Index 518