1 Introduction 1
1.1 Historical origins 2
1.2 General features 3
1.3 Basic string theory 6
1.4 Modern developments in superstring theory 9
2 The bosonic string 17
2.1 p-brane actions 17
2.2 The string action 24
2.3 String sigma-model action: the classical theory 30
2.4 Canonical quantization 36
2.5 Light-cone gauge quantization 48
3 Conformal field theory and string interactions 58
3.1 Conformal field theory 58
3.2 BRST quantization 75
3.3 Background fields 81
3.4 Vertex operators 85
3.5 The structure of string perturbation theory 89
3.6 The linear-dilaton vacuum and noncritical strings 98
3.7 Witten’s open-string field theory 100
4 Strings with world-sheet supersymmetry 109
4.1 Ramond–Neveu–Schwarz strings 110
4.2 Global world-sheet supersymmetry 112
4.3 Constraint equations and conformal invariance 118
4.4 Boundary conditions and mode expansions 122
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viii Contents
4.5 Canonical quantization of the RNS string 124
4.6 Light-cone gauge quantization of the RNS string 130
4.7 SCFT and BRST 140
5 Strings with space-time supersymmetry 148
5.1 The D0-brane action 149
5.2 The supersymmetric string action 155
5.3 Quantization of the GS action 160
5.4 Gauge anomalies and their cancellation 169
6 T-duality and D-branes 187
6.1 The bosonic string and Dp-branes 188
6.2 D-branes in type II superstring theories 203
6.3 Type I superstring theory 220
6.4 T-duality in the presence of background fields 227
6.5 World-volume actions for D-branes 229
7 The heterotic string 249
7.1 Nonabelian gauge symmetry in string theory 250
7.2 Fermionic construction of the heterotic string 252
7.3 Toroidal compactification 265
7.4 Bosonic construction of the heterotic string 286
8 M-theory and string duality 296
8.1 Low-energy effective actions 300
8.2 S-duality 323
8.3 M-theory 329
8.4 M-theory dualities 338
9 String geometry 354
9.1 Orbifolds 358
9.2 Calabi–Yau manifolds: mathematical properties 363
9.3 Examples of Calabi–Yau manifolds 366
9.4 Calabi–Yau compactifications of the heterotic string 374
9.5 Deformations of Calabi–Yau manifolds 385
9.6 Special geometry 391
9.7 Type IIA and type IIB on Calabi–Yau three-folds 399
9.8 Nonperturbative effects in Calabi–Yau compactifications 403
9.9 Mirror symmetry 411
9.10 Heterotic string theory on Calabi–Yau three-folds 415
9.11 K3 compactifications and more string dualities 418
9.12 Manifolds with G2 and Spin(7) holonomy 433
10 Flux compactifications 456
10.1 Flux compactifications and Calabi–Yau four-folds 460
10.2 Flux compactifications of the type IIB theory 480
Contents ix
10.3 Moduli stabilization 499
10.4 Fluxes, torsion and heterotic strings 508
10.5 The strongly coupled heterotic string 518
10.6 The landscape 522
10.7 Fluxes and cosmology 526
11 Black holes in string theory 549
11.1 Black holes in general relativity 552
11.2 Black-hole thermodynamics 562
11.3 Black holes in string theory 566
11.4 Statistical derivation of the entropy 582
11.5 The attractor mechanism 587
11.6 Small BPS black holes in four dimensions 599
12 Gauge theory/string theory dualities 610
12.1 Black-brane solutions in string theory and M-theory 613
12.2 Matrix theory 625
12.3 The AdS/CFT correspondence 638
12.4 Gauge/string duality for the conifold and generalizations 669
12.5 Plane-wave space-times and their duals 677
12.6 Geometric transitions 684
Bibliographic discussion 690
Bibliography 700
Index