String Theory in a Nutshell

by Kiritsis, Elias

• ISBN13: 9780691122304
• ISBN10: 069112230X
• Format: Hardcover
• Copyright: 2007-03-19
• Publisher: Princeton Univ Pr

Summary

This book is the essential new introduction to modern string theory, by one of the world's authorities on the subject. Concise, clearly presented, and up-to-date,String Theory in a Nutshellbrings together the best understood and most important aspects of a theory that has been evolving since the early 1980s. A core model of physics that substitutes one-dimensional extended "strings" for zero-dimensional point-like particles (as in quantum field theory), string theory has been the leading candidate for a theory that would successfully unify all fundamental forces of nature, including gravity. Starting with the basic definitions of the theory, Elias Kiritsis guides readers through classic and modern topics. In particular, he treats perturbative string theory and its Conformal Field Theory (CFT) tools in detail while also developing nonperturbative aspects and exploring the unity of string interactions. He presents recent topics including black holes, their microscopic entropy, and the AdS/CFT correspondence. He also describes matrix model tools for string theory. In all, the book contains nearly five hundred exercises for the graduate-level student, and works as a self-contained and detailed guide to the literature. String Theory in a Nutshellis the staple one-volume reference on the subject not only for students and researchers of theoretical high-energy physics, but also for mathematicians and physicists specializing in theoretical cosmology and QCD.

Author Biography

Elias Kiritsis is Directeur de Recherche at the CNRS, affiliated with the Ecole Polytechnique in Paris, and Professor of Physics at the University of Crete.

Table of Contents

Preface	p. xv
Abbreviations	p. xvii
Introduction	p. 1
Prehistory	p. 1
The Case for String Theory	p. 3
A Stringy Historical Perspective	p. 6
Conventions	p. 8
Bibliography	p. 9
Classical String Theory	p. 10
The Point Particle	p. 10
Relativistic Strings	p. 14
Oscillator Expansions	p. 20
Closed strings	p. 20
Open strings	p. 22
The Virasoro constraints	p. 24
Bibliography	p. 26
Exercises	p. 26
Quantization of Bosonic Strings	p. 28
Covariant Canonical Quantization	p. 28
Light-cone Quantization	p. 31
Spectrum of the Bosonic String	p. 32
Unoriented Strings	p. 33
Open strings and Chan-Paton factors	p. 34
Path Integral Quantization	p. 37
Topologically Nontrivial World-sheets	p. 39
BRST Primer	p. 40
BRST in String Theory and the Physical Spectrum	p. 42
Bibliography	p. 46
Exercises	p. 46
Conformal Field Theory	p. 49
Conformal Transformations	p. 49
The case of two dimensions	p. 51
Conformally Invariant Field Theory	p. 52
Radial Quantization	p. 54
Mode Expansions	p. 57
The Virasoro Algebra and the Central Charge	p. 58
The Hilbert Space	p. 59
The Free Boson	p. 60
The Free Fermion	p. 63
The Conformal Anomaly	p. 64
Representations of the Conformal Algebra	p. 66
Affine Current Algebras	p. 69
Free Fermions and O(N) Affine Symmetry	p. 71
Superconformal Symmetry	p. 77
N = (1,0)[subscript 2] superconformal symmetry	p. 77
N = (2,0)[subscript 2] superconformal symmetry	p. 79
N = (4,0)[subscript 2] superconformal symmetry	p. 81
Scalars with Background Charge	p. 82
The CFT of Ghosts	p. 84
CFT on the Disk	p. 86
Free massless bosons on the disk	p. 86
Free massless fermions on the disk	p. 88
The projective plane	p. 90
CFT on the Torus	p. 90
Compact Scalars	p. 93
Modular invariance	p. 97
Decompactification	p. 97
The torus propagator	p. 97
Marginal deformations	p. 98
Multiple compact scalars	p. 98
Enhanced symmetry and the string Brout-Englert-Higgs effect	p. 100
T-duality	p. 101
Free Fermions on the Torus	p. 103
Bosonization	p. 105
"Bosonization" of bosonic ghost system	p. 106
Orbifolds	p. 107
CFT on Other Surfaces of Euler Number Zero	p. 112
CFT on Higher-genus Riemann Surfaces	p. 116
Bibliography	p. 117
Exercises	p. 118
Scattering Amplitudes and Vertex Operators	p. 126
Physical Vertex Operators	p. 128
Calculation of Tree-level Tachyon Amplitudes	p. 130
The closed string	p. 130
The open string	p. 131
The One-loop Vacuum Amplitudes	p. 133
The torus	p. 134
The cylinder	p. 136
The Klein bottle	p. 138
The Mobius strip	p. 138
Tadpole cancellation	p. 139
UV structure and UV-IR correspondence	p. 140
Bibliography	p. 141
Exercises	p. 142
Strings in Background Fields	p. 144
The Nonlinear [sigma]-model Approach	p. 144
The Quest for Conformal Invariance	p. 147
Linear Dilaton and Strings in D < 26 Dimensions	p. 149
T-duality in Nontrivial Backgrounds	p. 151
Bibliography	p. 151
Exercises	p. 152
Superstrings and Supersymmetry	p. 155
N = (1,1)[subscript 2] World-sheet Superconformal Symmetry	p. 155
Closed (Type-II) Superstrings	p. 157
Massless R-R states	p. 159
Type-I Superstrings	p. 162
Heterotic Superstrings	p. 165
Superstring Vertex Operators	p. 168
One-loop Superstring Vacuum Amplitudes	p. 170
The type-IIA/B superstring	p. 170
The heterotic superstring	p. 171
The type-I superstring	p. 171
Closed Superstrings and T-duality	p. 174
The type-II string theories	p. 174
The heterotic string	p. 175
Supersymmetric Effective Actions	p. 175
Anomalies	p. 176
Bibliography	p. 182
Exercises	p. 183
D-branes	p. 187
Antisymmetric Tensors and p-branes	p. 187
Open Strings and T-duality	p. 188
D-branes	p. 191
D-branes and R-R Charges	p. 193
D-instantons	p. 196
D-brane Effective Actions	p. 197
The Dirac-Born-Infeld action	p. 197
Anomaly-related terms	p. 199
Multiple Branes and Nonabelian Symmetry	p. 200
T-duality and Orientifolds	p. 201
D-branes as Supergravity Solitons	p. 205
The supergravity solutions	p. 205
Horizons and singularities	p. 207
The extremal branes and their near-horizon geometry	p. 208
NS[subscript 5]-branes	p. 211
Bibliography	p. 213
Exercises	p. 213
Compactifications and Supersymmetry Breaking	p. 219
Narain Compactifications	p. 219
World-sheet versus Space-time Supersymmetry	p. 223
N = 1[subscript 4] space-time supersymmetry	p. 225
N = 2[subscript 4] space-time supersymmetry	p. 226
Orbifold Reduction of Supersymmetry	p. 228
A Heterotic Orbifold with N = 2[subscript 4] Supersymmetry	p. 231
Spontaneous Supersymmetry Breaking	p. 235
A Heterotic N = 1[subscript 4] Orbifold and Chirality in Four Dimensions	p. 237
Calabi-Yau Manifolds	p. 239
Holonomy	p. 241
Consequences of SU(3) holonomy	p. 242
The CY moduli space	p. 243
N = 1[subscript 4] Heterotic Compactifications	p. 245
The low-energy N = 1[subscript 4] heterotic spectrum	p. 246
K3 Compactification of the Type-II String	p. 247
N = 2[subscript 6] Orbifolds of the Type-II String	p. 250
CY Compactifications of Type-II Strings	p. 252
Mirror Symmetry	p. 253
Absence of Continuous Global Symmetries	p. 255
Orientifolds	p. 256
K3 orientifolds	p. 257
The Klein bottle amplitude	p. 258
D-branes on T[superscript 4]/Z[subscript 2]	p. 260
The cylinder amplitude	p. 263
The Mobius strip amplitude	p. 265
Tadpole cancellation	p. 266
The open string spectrum	p. 267
D-branes at Orbifold Singularities	p. 268
Magnetized Compactifications and Intersecting Branes	p. 271
Open strings in an internal magnetic field	p. 272
Intersecting branes	p. 277
Intersecting D[subscript 6]-branes	p. 278
Where is the Standard Model?	p. 280
The heterotic string	p. 280
Type-II string theory	p. 282
The type-I string	p. 283
Unification	p. 284
Bibliography	p. 286
Exercises	p. 287
Loop Corrections to String Effective Couplings	p. 294
Calculation of Heterotic Gauge Thresholds	p. 296
On-shell Infrared Regularization	p. 301
Evaluation of the threshold	p. 303
Heterotic Gravitational Thresholds	p. 304
One-loop Fayet-Iliopoulos Terms	p. 305
N = 1,2[subscript 4] Examples of Threshold Corrections	p. 309
N = 2[subscript 4] Universality of Thresholds	p. 312
Unification Revisited	p. 315
Bibliography	p. 317
Exercises	p. 317
Duality Connections and Nonperturbative Effects	p. 320
Perturbative Connections	p. 322
BPS States and BPS Bounds	p. 323
Nonrenormalization Theorems and BPS-saturated Couplings	p. 325
Type-IIA versus M-theory	p. 328
Self-duality of the Type-IIB String	p. 331
U-duality of Type-Il String Theory	p. 334
U-duality and bound states	p. 335
Heterotic/Type I Duality in Ten Dimensions	p. 336
The type-I D[subscript 1]-string	p. 339
The type-I D[subscript 5]-brane	p. 341
Further consistency checks	p. 343
M-theory and the E[subscript 8] x E[subscript 8] Heterotic String	p. 344
Unification at strong heterotic coupling	p. 347
Heterotic/Type II Duality in Six Dimensions	p. 348
Gauge symmetry enhancement and singular K3 surfaces	p. 352
Heterotic/type II duality in four dimensions	p. 355
Conifold Singularities and Conifold Transitions	p. 356
Bibliography	p. 362
Exercises	p. 363
Black Holes and Entropy in String Theory	p. 369
A Brief History	p. 369
The Strategy	p. 369
Black-hole Thermodynamics	p. 371
The Euclidean continuation	p. 372
Hawking evaporation and greybody factors	p. 374
The Information Problem and the Holographic Hypothesis	p. 375
Five-dimensional Extremal Charged Black Holes	p. 377
Five-dimensional Nonextremal RN Black Holes	p. 379
The Near-horizon Region	p. 381
Semiclassical Derivation of the Hawking Rate	p. 383
The Microscopic Realization	p. 386
The world-volume theory of the bound state	p. 387
The low-energy SCFT of the D[subscript 1]-D[subscript 5] bound state	p. 389
Microscopic calculation of the entropy	p. 391
Microscopic derivation of Hawking evaporation rates	p. 394
Epilogue	p. 396
Bibliography	p. 398
Exercises	p. 399
The Bulk/Boundary Correspondence	p. 403
Large-N Gauge Theories and String Theory	p. 405
The Decoupling Principle	p. 408
The Near-horizon Limit	p. 409
Elements of the Correspondence	p. 410
Bulk Fields and Boundary Operators	p. 413
Holography	p. 416
Testing the AdS[subscript 5]/CFT[subscript 4] Correspondence	p. 417
The chiral spectrum of N = 4 gauge theory	p. 418
Matching to the string theory spectrum	p. 420
N = 8 five-dimensional gauged supergravity	p. 422
Protected correlation functions and anomalies	p. 422
Correlation Functions	p. 424
Two-point functions	p. 425
Three-point functions	p. 427
The gravitational action and the conformal anomaly	p. 428
Wilson Loops	p. 433
AdS[subscript 5]/CFT[subscript 4] Correspondence at Finite Temperature	p. 436
N = 4 super Yang-Mills theory at finite temperature	p. 436
The near-horizon limit of black D[subscript 3]-branes	p. 438
Finite-volume and large-N phase transitions	p. 440
Thermal holographic physics	p. 443
Spatial Wilson loops in (a version of) QCD[subscript 3]	p. 444
The glueball mass spectrum	p. 446
AdS[subscript 3]/CFT[subscript 2] Correspondence	p. 447
The greybody factors revisited	p. 450
The Holographic Renormalization Group	p. 450
Perturbations of the CFT[subscript 4]	p. 451
Domain walls and flow equations	p. 452
A RG flow preserving N = 1 supersymmetry	p. 454
The Randall-Sundrum Geometry	p. 456
An alternative to compactification	p. 459
Bibliography	p. 462
Exercises	p. 463
String Theory and Matrix Models	p. 470
M(atrix) Theory	p. 471
Membrane quantization	p. 471
Type-IIA D[subscript 0]-branes and DLCQ	p. 473
Gravitons and branes in M(atrix) theory	p. 476
The two-graviton interaction from M(atrix) theory	p. 477
Matrix Models and D = 1 Bosonic String Theory	p. 479
The continuum limit	p. 481
Solving the matrix model	p. 482
The double-scaling limit	p. 485
The free-fermion picture	p. 487
Matrix Description of D = 2 String Theory	p. 488
Matrix quantum mechanics and free fermions on the line	p. 490
The continuum limit	p. 492
The double-scaling limit	p. 494
D-particles, tachyons, and holography	p. 496
Bibliography	p. 498
Exercises	p. 498
Two-dimensional Complex Geometry	p. 503
Differential Forms	p. 505
Theta and Other Elliptic Functions	p. 507
[theta] and Related Functions	p. 507
The Weierstrass Function	p. 510
Modular Forms	p. 510
Poisson Resummation	p. 512
Toroidal Lattice Sums	p. 513
Toroidal Kaluza-Klein Reduction	p. 516
The Reissner-Nordstrom Black Hole	p. 519
Electric-magnetic Duality in D = 4	p. 522
Supersymmetric Actions in Ten and Eleven Dimensions	p. 525
The N = 1[subscript 11] Supergravity	p. 526
Type-IIA Supergravity	p. 527
Type-IIB Supergravity	p. 528
Type-II Supergravities: The Democratic Formulation	p. 529
N = 1[subscript 10] Supersymmetry	p. 530
N = 1,2, Four-dimensional Supergravity Coupled to Matter	p. 533
N = 1[subscript 4] Supergravity	p. 533
N = 2[subscript 4] Supergravity	p. 535
BPS Multiplets in Four Dimensions	p. 537
The Geometry of Anti-de Sitter Space	p. 541
The Minkowski Signature AdS	p. 541
Euclidean AdS	p. 544
The Conformal Structure of Flat Space	p. 546
Fields in AdS	p. 548
The wave equation in Poincare coordinates	p. 549
The bulk-boundary propagator	p. 550
The bulk-to-bulk propagator	p. 551
Bibliography	p. 553
Index	p. 575
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