Supersymmetry and String Theory: Beyond the Standard Model

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 17
A note on choice of metric......Page 20
Text website......Page 22
Part 1 Effective field theory: the Standard Model, supersymmetry, unification......Page 23
1 Before the Standard Model......Page 25
Suggested reading......Page 29
2.1 Yang–Mills theory......Page 31
2.2.1 The Goldstone phenomenon......Page 34
2.2.2 Aside: choosing a vacuum......Page 36
2.2.3 The Higgs mechanism......Page 38
2.2.4 Goldstone and Higgs phenomena for non-Abelian symmetries......Page 39
2.3 The quantization of Yang–Mills theories......Page 40
2.3.1 Gauge fixing in theories with broken gauge symmetry......Page 42
2.4 The particles and fields of the Standard Model......Page 44
2.5 The gauge boson masses......Page 47
2.6 Quark and lepton masses......Page 49
Exercises......Page 50
3.1 The weak interactions......Page 51
3.2 The quark and lepton mass matrices......Page 54
3.3 The strong interactions......Page 56
3.4 The renormalization group......Page 57
3.5 Calculating the beta function......Page 61
3.6 The strong interactions and dimensional transmutation......Page 65
3.7 Confinement and lattice gauge theory......Page 66
3.7.1 Wilson’s formulation of lattice gauge theory......Page 68
3.8.1 e+e Annihilation......Page 73
3.8.2 Jets in e+e annihilation......Page 76
3.8.3 Deep inelastic scattering......Page 78
Suggested reading......Page 81
Exercises......Page 83
4 The Standard Model as an effective field theory......Page 85
4.0.1 Integrating out the W and Z bosons......Page 86
4.0.2 What might the Standard Model come from?......Page 87
4.1.1 Dimension five: lepton number violation and neutrino mass......Page 88
4.1.2 Other symmetry-breaking dimension-five operators......Page 90
4.1.3 Irrelevant operators and high-precision experiments......Page 91
4.2 Challenges for the Standard Model......Page 92
4.3 The hierarchy problem......Page 93
4.4 Dark matter and dark energy......Page 94
Suggested reading......Page 95
5 Anomalies, instantons and the strong CP problem......Page 97
5.1 The chiral anomaly......Page 98
5.1.2 Return to QCD......Page 102
5.2.1 The anomaly in two dimensions......Page 103
5.2.2 Path integral computation of the anomaly......Page 105
5.2.3 The CPN model: an asymptotically free theory......Page 106
5.2.4 The large-N limit......Page 107
5.2.5 The role of instantons......Page 108
5.3.1 The theory and its symmetries......Page 111
5.3.2 Instantons in QCD......Page 113
5.3.3 Physical interpretation of the instanton solution......Page 119
5.3.4 QCD and the U(1) problem......Page 121
5.4.1 The θ-dependence of the vacuum energy......Page 122
5.4.2 The neutron electric dipole moment......Page 123
5.5.1 When mu = 0......Page 124
5.5.3 The axion......Page 125
Suggested reading......Page 127
Exercises......Page 128
6 Grand unification......Page 129
6.2 Renormalization of couplings......Page 132
6.3 Breaking to SU(3) × SU(2) × U(1)......Page 133
6.4 SU(2) × U(1) breaking......Page 134
6.5 Charge quantization and magnetic monopoles......Page 135
6.7 Other groups......Page 136
Exercises......Page 139
7 Magnetic monopoles and solitons......Page 141
7.1 Solitons in 1 + 1 dimensions......Page 142
7.3 Magnetic monopoles......Page 144
7.4 The BPS limit......Page 146
7.5 Collective coordinates for the monopole solution......Page 147
7.6 The Witten effect: the electric charge in the presence of Theta......Page 149
7.7 Electric–magnetic duality......Page 150
Exercises......Page 151
8 Technicolor: a first attempt to explain hierarchies......Page 153
8.1 QCD in a world without Higgs fields......Page 154
8.2 Fermion masses: extended technicolor......Page 155
8.3 Precision electroweak measurements......Page 157
Exercises......Page 158
Part 2 Supersymmetry......Page 159
9 Supersymmetry......Page 161
9.2 Superspace......Page 162
9.3 N = 1 Lagrangians......Page 166
9.4 The supersymmetry currents......Page 169
9.5 The ground-state energy in globally supersymmetric theories......Page 170
9.6.1 The Wess–Zumino model......Page 171
9.6.2 A U(1) gauge theory......Page 172
9.7 Non-renormalization theorems......Page 173
9.8 Local supersymmetry: supergravity......Page 176
Exercises......Page 177
10.1 Spontaneous supersymmetry breaking......Page 179
10.1.1 The Fayet–Iliopoulos D term......Page 180
10.2 The goldstino theorem......Page 182
10.3 Loop corrections and the vacuum degeneracy......Page 183
10.4 Explicit, soft supersymmetry breaking......Page 184
10.5 Supersymmetry breaking in supergravity models......Page 185
Exercises......Page 188
11 The Minimal Supersymmetric Standard Model......Page 189
11.1 Soft supersymmetry breaking in the MSSM......Page 191
11.1.1 Cancellation of quadratic divergences in gauge theories......Page 193
11.2 SU(2) × U(1) breaking......Page 195
11.3 Why is one Higgs mass negative?......Page 197
11.4 Radiative corrections to the Higgs mass limit......Page 198
11.5 Embedding the MSSM in supergravity......Page 199
11.6 The term......Page 200
11.7.1 Direct searches for supersymmetric particles......Page 201
11.7.2 Constraints from rare processes......Page 202
Exercises......Page 205
12.1 A supersymmetric grand unified model......Page 207
12.2 Coupling constant unification......Page 208
12.3 Dimension-five operators and proton decay......Page 210
Exercises......Page 211
13 Supersymmetric dynamics......Page 213
13.1 Criteria for supersymmetry breaking: the Witten index......Page 214
13.2 Gaugino condensation in pure gauge theories......Page 215
13.3 Supersymmetric QCD......Page 216
13.4 N < N: a non-perturbative superpotential......Page 219
13.4.1 The Lambda -dependence of the superpotential......Page 221
13.5 The superpotential in the case N < N – 1......Page 222
13.6 N = N - 1: the instanton-generated superpotential......Page 223
13.6.1 An application of the instanton result: gaugino condensation......Page 229
Exercises......Page 230
14.1 Models of dynamical supersymmetry breaking......Page 231
14.1.1 The (3, 2) model......Page 232
14.2.1 Gravity mediation and dynamical supersymmetry breaking: anomaly mediation......Page 233
Minimal Gauge Mediation (MGM)......Page 236
Exercises......Page 240
15.1 N = 2 theories: exact moduli spaces......Page 241
15.2 A still simpler theory: N = 4 Yang–Mills......Page 243
15.3 A deeper understanding of the BPS condition......Page 245
15.3.1 N = 4 Yang–Mills theories and electric–magnetic duality......Page 246
15.4 Seiberg–Witten theory......Page 247
Suggested reading......Page 252
Exercises......Page 253
16.1 Conformally invariant field theories......Page 255
16.2 More supersymmetric QCD......Page 257
16.3 N = N......Page 258
16.3.1 Supersymmetry breaking in quantum moduli spaces......Page 259
16.3.2 N = N + 1......Page 260
16.4 N > N + 1......Page 262
Suggested reading......Page 263
Exercises......Page 264
17 An introduction to general relativity......Page 265
17.1 Tensors in general relativity......Page 266
17.2 Curvature......Page 271
17.3 The gravitational action......Page 272
17.4 The Schwarzschild solution......Page 274
17.5 Features of the Schwarzschild metric......Page 276
17.6 Coupling spinors to gravity......Page 278
Exercises......Page 279
18 Cosmology......Page 281
18.1 A history of the universe......Page 285
Exercises......Page 290
19 Astroparticle physics and inflation......Page 291
19.1 Inflation......Page 294
19.1.1 Fluctuations: the formation of structure......Page 297
19.1.2 Models of Inflation......Page 299
19.1.3 Constraints on reheating: the gravitino problem......Page 301
19.2 The axion as dark matter......Page 302
19.3 The LSP as the dark matter......Page 305
19.4 The moduli problem......Page 307
19.5.1 Baryogenesis through heavy particle decays......Page 309
19.5.2 Electroweak baryogenesis......Page 310
19.5.3 Leptogenesis......Page 312
19.5.4 Baryogenesis through coherent scalar fields......Page 314
19.6 Flat directions and baryogenesis......Page 316
19.7 Supersymmetry breaking in the early universe......Page 318
19.8 The fate of the condensate......Page 319
19.9 Dark energy......Page 322
Exercises......Page 323
Part 3 String theory......Page 325
20 Introduction......Page 327
20.1 The peculiar history of string theory......Page 328
Suggested reading......Page 333
21 The bosonic string......Page 335
21.1.1 Open strings......Page 337
21.2 Closed strings......Page 340
21.3.1 String theory in conformal gauge......Page 342
21.4 Conformal invariance......Page 344
21.5 Vertex operators and the S-matrix......Page 350
21.5.1 Vertex operators......Page 351
21.5.2 The S-matrix......Page 352
21.5.3 Factorization......Page 355
21.6 The S-matrix vs. the effective action......Page 356
21.7 Loop amplitudes......Page 357
Exercises......Page 360
22.1 Open superstrings......Page 363
22.2 Quantization in the Ramond sector: the appearance of space-time fermions......Page 365
22.3 Type II theory......Page 366
22.4 World sheet supersymmetry......Page 367
22.5.1 The normal ordering constants......Page 368
22.5.2 The different sectors of the Type II theory......Page 369
22.5.3 Other possibilities: modular invariance and the GSO projection......Page 371
22.5.4 More on the Type I theory: gauge groups......Page 374
22.6 Manifest space-time supersymmetry: the Green–Schwarz formalism......Page 375
22.7 Vertex operators......Page 377
Exercises......Page 378
23 The heterotic string......Page 381
23.1 The O(32) theory......Page 382
23.3 Heterotic string interactions......Page 383
Suggested reading......Page 385
Exercises......Page 386
24.0.1 Eleven-dimensional supergravity......Page 387
24.0.3 Ten-dimensional Yang–Mills theory......Page 389
24.1.1 Couplings in closed string theories......Page 390
24.1.3 Effective Lagrangian argument......Page 391
24.1.4 World sheet coupling of the dilaton......Page 392
Exercise......Page 393
25.1 Compactification in field theory: the Kaluza–Klein program......Page 395
25.1.1 Generalizations and limitations of the Kaluza–Klein program......Page 398
25.2 Closed strings on tori......Page 399
25.3 Enhanced symmetries......Page 402
25.4 Strings in background fields......Page 404
25.4.1 The beta function......Page 405
25.4.2 More general tori......Page 407
25.5 Bosonic formulation of the heterotic string......Page 408
25.6 Orbifolds......Page 409
25.6.1 Discrete symmetries......Page 415
25.6.2 Modular invariance, interactions in orbifold constructions......Page 416
25.7 Effective actions in four dimensions for orbifold models......Page 417
25.8 Non-supersymmetric compactifications......Page 420
Suggested reading......Page 421
Exercises......Page 422
26.1 Mathematical preliminaries......Page 423
26.2 Calabi–Yau spaces: constructions......Page 428
26.3 The spectrum of Calabi–Yau compactifications......Page 431
26.4 World sheet description of Calabi–Yau compactification......Page 433
26.5 An example: the quintic in CP4......Page 436
26.6 Calabi–Yau compactification of the heterotic string at weak coupling......Page 438
26.6.1 Features of Calabi–Yau compactifications of the heterotic string......Page 439
26.6.2 Gauge groups: symmetry breaking......Page 441
26.6.4 Continuous global symmetries......Page 443
26.6.5 Discrete symmetries......Page 444
26.6.6 Further symmetry breaking: the Standard Model gauge group......Page 445
26.6.7 Gauge coupling unification......Page 446
26.6.8 Calculating the parameters of the low-energy Lagrangian......Page 447
Suggested reading......Page 448
Exercises......Page 449
27 Dynamics of string theory at weak coupling......Page 451
27.1 Non-renormalization theorems......Page 452
27.1.1 Non-renormalization theorems for world sheet perturbation theory......Page 453
27.1.2 Non-renormalization theorems for string perturbation theory......Page 455
27.2 Fayet–Iliopoulos D-terms......Page 456
27.3 Gaugino condensation......Page 460
27.4 Obstacles to a weakly coupled string phenomenology......Page 461
Suggested reading......Page 462
28 Beyond weak coupling: non-perturbative string theory......Page 463
28.2 Strings at strong coupling: duality......Page 464
28.3 D-branes......Page 465
28.3.1 Brane charges......Page 468
28.4 Branes from T-duality of Type I strings......Page 469
28.4.1 Orientifolds......Page 472
28.5 Strong–weak coupling dualities: the equivalence of different string theories......Page 473
28.6.1 IIA→ eleven-dimensional supergravity (M theory)......Page 474
28.6.2 IIB self-duality......Page 478
28.6.3 Type I –O(32) duality......Page 479
28.7 Strongly coupled heterotic string......Page 480
28.7.1 Compactification of the strongly coupled heterotic string......Page 481
28.8 Non-perturbative formulations of string theory......Page 482
28.8.1 Matrix theory......Page 483
A little more general relativity: anti-de Sitter space......Page 485
Maldacena’s conjecture......Page 486
Suggested reading......Page 487
Exercises......Page 488
29.1 Large extra dimensions: the ADD proposal......Page 489
29.2 Warped spaces: the Randall–Sundrum proposal......Page 492
Exercise......Page 495
30 Coda: Where are We Headed?......Page 497
Suggested reading......Page 501
Part 4 The appendices......Page 503
Appendix A Two-component spinors......Page 505
Appendix B Goldstone’s theorem and the pi mesons......Page 509
Exercises......Page 511
C.1 Path integral review......Page 513
C.2 Finite-temperature field theory......Page 514
C.3 QCD at high temperature......Page 517
C.4 Weak interactions at high temperature......Page 518
C.5 Electroweak baryon number violation......Page 519
Exercises......Page 521
Appendix D The beta function in supersymmetric Yang–Mills theory......Page 523
Exercise......Page 525
References......Page 527
Index......Page 533