String Theory in a Nutshell Book

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