A First Course in String Theory, Second Edition

✍ Scribed by Barton Zwiebach

• Year: 2009
• Tongue: English
• Leaves: 697
• Edition: 2nd
• Category: Library

✦ Synopsis

Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. Complete and thorough in its coverage, the author presents the main concepts of string theory in a concrete and physical way in order to develop intuition before formalism, often through simplified and illustrative examples. This new edition now includes AdS/CFT correspondence, which is the hottest area of string theory right now as well as introducing superstrings. The text is perfectly suited to introductory courses in string theory for students with a background in mathematics and physics. New sections cover strings on orbifolds, cosmic strings, moduli stabilization, and the string theory landscape.

✦ Table of Contents

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Foreword......Page 15
Acknowledgements......Page 17
About this book......Page 21
This book as a textbook......Page 24
PART I BASICS......Page 25
1.1 The road to unification......Page 27
1.2 String theory as a unified theory of physics......Page 30
1.3 String theory and its verification......Page 33
1.4 Developments and outlook......Page 35
2.1 Units and parameters......Page 37
2.2 Intervals and Lorentz transformations......Page 39
2.3 Light-cone coordinates......Page 46
2.4 Relativistic energy and momentum......Page 50
2.5 Light-cone energy and momentum......Page 52
2.6 Lorentz invariance with extra dimensions......Page 54
2.7 Compact extra dimensions......Page 55
2.8 Orbifolds......Page 59
2.9 Quantum mechanics and the square well......Page 60
2.10 Square well with an extra dimension......Page 62
Problems......Page 64
3.1 Classical electrodynamics......Page 69
3.2 Electromagnetism in three dimensions......Page 71
3.3 Manifestly relativistic electrodynamics......Page 72
3.4 An aside on spheres in higher dimensions......Page 76
3.5 Electric fields in higher dimensions......Page 79
3.6 Gravitation and Planck's length......Page 82
3.7 Gravitational potentials......Page 86
3.8 The Planck length in various dimensions......Page 87
3.9 Gravitational constants and compactification......Page 88
3.10 Large extra dimensions......Page 91
Problems......Page 93
4.1 Equations of motion for transverse oscillations......Page 97
4.2 Boundary conditions and initial conditions......Page 99
4.3 Frequencies of transverse oscillation......Page 100
4.4 More general oscillating strings......Page 101
4.5 A brief review of Lagrangian mechanics......Page 102
4.6 The nonrelativistic string Lagrangian......Page 105
Problems......Page 109
5.1 Action for a relativistic point particle......Page 113
5.2 Reparameterization invariance......Page 117
5.3 Equations of motion......Page 118
5.4 Relativistic particle with electric charge......Page 121
Problems......Page 122
6.1 Area functional for spatial surfaces......Page 124
6.2 Reparameterization invariance of the area......Page 127
6.3 Area functional for spacetime surfaces......Page 130
6.4 The Nambu-Goto string action......Page 135
6.5 Equations of motion, boundary conditions, and D-branes......Page 136
6.6 The static gauge......Page 140
6.7 Tension and energy of a stretched string......Page 142
6.8 Action in terms of transverse velocity......Page 144
6.9 Motion of open string endpoints......Page 148
Problems......Page 149
7.1 Choosing a parameterization......Page 154
7.2 Physical interpretation of the string equation of motion......Page 156
7.3 Wave equation and constraints......Page 158
7.4 General motion of an open string......Page 160
7.5 Motion of closed strings and cusps......Page 166
7.6 Cosmic strings......Page 169
Problems......Page 173
8.1 Electric charge conservation......Page 178
8.2 Conserved charges from Lagrangian symmetries......Page 179
8.3 Conserved currents on the world-sheet......Page 183
8.4 The complete momentum current......Page 185
8.5 Lorentz symmetry and associated currents......Page 189
8.6 The slope parameter Alpha......Page 192
Problems......Page 194
9.1 A class of choices for Tau......Page 199
9.2 The associated Alpha parameterization......Page 202
9.3 Constraints and wave equations......Page 206
9.4 Wave equation and mode expansions......Page 207
9.5 Light-cone solution of equations of motion......Page 210
Problems......Page 215
10.1 Introduction......Page 218
10.2 An action for scalar fields......Page 219
10.3 Classical plane-wave solutions......Page 221
10.4 Quantum scalar fields and particle states......Page 224
10.5 Maxwell fields and photon states......Page 230
10.6 Gravitational fields and graviton states......Page 233
Problems......Page 237
11.1 Light-cone point particle......Page 240
11.2 Heisenberg and Schrödinger pictures......Page 242
11.3 Quantization of the point particle......Page 244
11.4 Quantum particle and scalar particles......Page 249
11.5 Light-cone momentum operators......Page 250
11.6 Light-cone Lorentz generators......Page 253
Problems......Page 257
12.1 Light-cone Hamiltonian and commutators......Page 260
12.2 Commutation relations for oscillators......Page 265
12.3 Strings as harmonic oscillators......Page 270
12.4 Transverse Virasoro operators......Page 274
12.5 Lorentz generators......Page 283
12.6 Constructing the state space......Page 286
12.7 Equations of motion......Page 292
12.8 Tachyons and D-brane decay......Page 294
Problems......Page 298
13.1 Mode expansions and commutation relations......Page 304
13.2 Closed string Virasoro operators......Page 310
13.3 Closed string state space......Page 314
13.4 String coupling and the dilaton......Page 318
13.5 Closed strings on the…......Page 320
13.6 The twisted sector of the orbifold......Page 322
Problems......Page 327
14.1 Introduction......Page 331
14.2 Anticommuting variables and operators......Page 332
14.3 World-sheet fermions......Page 333
14.4 Neveu–Schwarz sector......Page 336
14.5 Ramond sector......Page 339
14.6 Counting states......Page 341
14.7 Open superstrings......Page 344
14.8 Closed string theories......Page 346
Problems......Page 349
PART II DEVELOPMENTS......Page 353
15.1 Dp-branes and boundary conditions......Page 355
15.2 Quantizing open strings on Dp-branes......Page 357
15.3 Open strings between parallel Dp-branes......Page 362
15.4 Strings between parallel Dp- and Dq-branes......Page 369
Problems......Page 375
16.1 Fundamental string charge......Page 380
16.2 Visualizing string charge......Page 386
16.3 Strings ending on D-branes......Page 389
16.4 D-brane charges......Page 394
Problems......Page 397
17.1 Duality symmetries and Hamiltonians......Page 400
17.2 Winding closed strings......Page 402
17.3 Left movers and right movers......Page 405
17.4 Quantization and commutation relations......Page 407
17.5 Constraint and mass formula......Page 410
17.6 State space of compactified closed strings......Page 412
17.7 A striking spectrum coincidence......Page 416
17.8 Duality as a full quantum symmetry......Page 418
Problems......Page 421
18.1 T-duality and D-branes......Page 424
18.2 U(1) gauge transformations......Page 428
18.3 Wilson lines on circles......Page 430
18.4 Open strings and Wilson lines......Page 434
Problems......Page 437
19.1 Maxwell fields coupling to open strings......Page 439
19.2 D-branes with electric fields......Page 442
19.3 D-branes with magnetic fields......Page 447
Problems......Page 453
20.1 The framework of nonlinear electrodynamics......Page 457
20.2 Born-Infeld electrodynamics......Page 462
20.3 Born-Infeld theory and T-duality......Page 467
Problems......Page 470
21.1 Intersecting D6-branes......Page 475
21.2 D-branes and the Standard Model gauge group......Page 481
21.3 Open strings and the Standard Model fermions......Page 487
21.4 The Standard Model on intersecting D6-branes......Page 496
21.5 String theory models of particle physics......Page 503
21.6 Moduli stabilization and the landscape......Page 505
Problems......Page 514
22.1 A review of statistical mechanics......Page 519
22.2 Partitions and the quantum violin string......Page 522
22.3 Hagedorn temperature......Page 529
22.4 Relativistic particle partition function......Page 531
22.5 Single string partition function......Page 533
22.6 Black holes and entropy......Page 537
22.7 Counting states of a black hole......Page 541
Problems......Page 545
23.1 Introduction......Page 549
23.2 Mesons and quantum rotating strings......Page 550
23.3 The energy of a stretched effective string......Page 555
23.4 A large-N limit of a gauge theory......Page 557
23.5 Gravitational effects of massive sources......Page 559
23.6 Motivating the AdS/CFT correspondence......Page 561
23.7 Parameters in the AdS/CFT correspondence......Page 565
23.8 Hyperbolic spaces and conformal boundary......Page 567
23.9 Geometry of AdS and holography......Page 573
23.10 AdS/CFT at finite temperature......Page 578
23.11 The quark-gluon plasma......Page 583
Problems......Page 585
24.1 Introduction......Page 592
24.2 Open string Virasoro operators......Page 594
24.3 Selecting the quantum constraints......Page 596
24.4 Lorentz covariant state space......Page 601
24.5 Closed string Virasoro operators......Page 604
24.6 The Polyakov string action......Page 606
Problems......Page 611
25.1 Introduction......Page 615
25.2 Interactions and observables......Page 616
25.3 String interactions and global world-sheets......Page 619
25.4 World-sheets as Riemann surfaces......Page 622
25.5 Schwarz-Christoffel map and three-string interaction......Page 626
25.6 Moduli spaces of Riemann surfaces......Page 632
25.7 Four open string interaction......Page 641
25.8 Veneziano amplitude......Page 646
Problems......Page 650
26.1 Loop diagrams and ultraviolet divergences......Page 654
26.2 Annuli and one-loop open strings......Page 655
26.3 Annuli and electrostatic capacitance......Page 660
26.4 Non-planar open string diagrams......Page 666
26.5 Four closed string interactions......Page 667
26.6 The moduli space of tori......Page 670
Problems......Page 680
References......Page 683
References......Page 685
Index......Page 691

✦ Subjects

Физика;Квантовая физика;Физика элементарных частиц и полей;Квантовая теория поля;Теория струн;