Supersymmetry And String Theory. Beyond The Standard Model – Michael Dine – 1st Edition

Preface page xv
A note on choice of metric xviii
Text website xx
Part 1 Effective field theory: the Standard Model,
supersymmetry, unification 1
1 Before the Standard Model 3
Suggested reading 7
2 The Standard Model 9
2.1 Yang–Mills theory 9
2.2 Realizations of symmetry in quantum field theory 12
2.3 The quantization of Yang–Mills theories 18
2.4 The particles and fields of the Standard Model 22
2.5 The gauge boson masses 25
2.6 Quark and lepton masses 27
Suggested reading 28
Exercises 28
3 Phenomenology of the Standard Model 29
3.1 The weak interactions 29
3.2 The quark and lepton mass matrices 32
3.3 The strong interactions 34
3.4 The renormalization group 35
3.5 Calculating the beta function 39
3.6 The strong interactions and dimensional
transmutation 43
3.7 Confinement and lattice gauge theory 44
3.8 Strong interaction processes at high momentum transfer 51
Suggested reading 59
Exercises 61
4 The Standard Model as an effective field theory 63
4.1 Lepton and baryon number violation 66
4.2 Challenges for the Standard Model 70
4.3 The hierarchy problem 71
4.4 Dark matter and dark energy 72
4.5 Summary: successes and limitations of the
Standard Model 73
Suggested reading 73
5 Anomalies, instantons and the strong CP problem 75
5.1 The chiral anomaly 76
5.2 A two-dimensional detour 81
5.3 Real QCD 89
5.4 The strong CP problem 100
5.5 Possible solutions of the strong CP problem 102
Suggested reading 105
Exercises 106
6 Grand unification 107
6.1 Cancellation of anomalies 110
6.2 Renormalization of couplings 110
6.3 Breaking to SU(3) × SU(2) × U(1) 111
6.4 SU(2) × U(1) breaking 112
6.5 Charge quantization and magnetic monopoles 113
6.6 Proton decay 114
6.7 Other groups 114
Suggested reading 117
Exercises 117
7 Magnetic monopoles and solitons 119
7.1 Solitons in 1 + 1 dimensions 120
7.2 Solitons in 2 + 1 dimensions: strings or vortices 122
7.3 Magnetic monopoles 122
7.4 The BPS limit 124
7.5 Collective coordinates for the monopole solution 125
7.6 The Witten effect: the electric charge in the
presence of ? 127
7.7 Electric–magnetic duality 128
Suggested reading 129
Exercises 129
8 Technicolor: a first attempt to explain hierarchies 131
8.1 QCD in a world without Higgs fields 132
8.2 Fermion masses: extended technicolor 133
8.3 Precision electroweak measurements 135
Suggested reading 136
Exercises 136
Part 2 Supersymmetry 137
9 Supersymmetry 139
9.1 The supersymmetry algebra and its representations 140
9.2 Superspace 140
9.3 N = 1 Lagrangians 144
9.4 The supersymmetry currents 147
9.5 The ground-state energy in globally supersymmetric
theories 148
9.6 Some simple models 149
9.7 Non-renormalization theorems 151
9.8 Local supersymmetry: supergravity 154
Suggested reading 155
Exercises 155
10 A first look at supersymmetry breaking 157
10.1 Spontaneous supersymmetry breaking 157
10.2 The goldstino theorem 160
10.3 Loop corrections and the vacuum degeneracy 161
10.4 Explicit, soft supersymmetry breaking 162
10.5 Supersymmetry breaking in supergravity models 163
Suggested reading 166
Exercises 166
11 The Minimal Supersymmetric Standard Model 167
11.1 Soft supersymmetry breaking in the MSSM 169
11.2 SU(2) × U(1) breaking 173
11.3 Why is one Higgs mass negative? 175
11.4 Radiative corrections to the Higgs mass limit 176
11.5 Embedding the MSSM in supergravity 177
11.6 The µ term 178
11.7 Constraints on soft breakings 179
Suggested reading 183
Exercises 183
12 Supersymmetric grand unification 185
12.1 A supersymmetric grand unified model 185
12.2 Coupling constant unification 186
12.3 Dimension-five operators and proton decay 188
Suggested reading 189
Exercises 189
13 Supersymmetric dynamics 191
13.1 Criteria for supersymmetry breaking: the Witten index 192
13.2 Gaugino condensation in pure gauge theories 193
13.3 Supersymmetric QCD 194
13.4 Nf < N: a non-perturbative superpotential 197
13.5 The superpotential in the case Nf < N ? 1 200
13.6 Nf = N ? 1: the instanton-generated superpotential 201
Suggested reading 208
Exercises 208
14 Dynamical supersymmetry breaking 209
14.1 Models of dynamical supersymmetry breaking 209
14.2 Particle physics and dynamical supersymmetry breaking 211
Suggested reading 218
Exercises 218
15 Theories with more than four conserved supercharges 219
15.1 N = 2 theories: exact moduli spaces 219
15.2 A still simpler theory: N = 4 Yang–Mills 221
15.3 A deeper understanding of the BPS condition 223
15.4 Seiberg–Witten theory 225
Suggested reading 230
Exercises 231
16 More supersymmetric dynamics 233
16.1 Conformally invariant field theories 233
16.2 More supersymmetric QCD 235
16.3 Nf = Nc 236
16.4 Nf > N + 1 240
16.5 Nf ? 3/2N 241
Suggested reading 241
Exercises 242
17 An introduction to general relativity 243
17.1 Tensors in general relativity 244
17.2 Curvature 249
17.3 The gravitational action 250
17.4 The Schwarzschild solution 252
17.5 Features of the Schwarzschild metric 254
17.6 Coupling spinors to gravity 256
Suggested reading 257
Exercises 257
18 Cosmology 259
18.1 A history of the universe 263
Suggested reading 268
Exercises 268
19 Astroparticle physics and inflation 269
19.1 Inflation 272
19.2 The axion as dark matter 280
19.3 The LSP as the dark matter 283
19.4 The moduli problem 285
19.5 Baryogenesis 287
19.6 Flat directions and baryogenesis 294
19.7 Supersymmetry breaking in the early universe 296
19.8 The fate of the condensate 297
19.9 Dark energy 300
Suggested reading 301
Exercises 301
Part 3 String theory 303
20 Introduction 305
20.1 The peculiar history of string theory 306
Suggested reading 311
21 The bosonic string 313
21.1 The light cone gauge in string theory 315
21.2 Closed strings 318
21.3 String interactions 320
21.4 Conformal invariance 322
21.5 Vertex operators and the S-matrix 328
21.6 The S-matrix vs. the effective action 334
21.7 Loop amplitudes 335
Suggested reading 338
Exercises 338
22 The superstring 341
22.1 Open superstrings 341
22.2 Quantization in the Ramond sector: the appearance of
space-time fermions 343
22.3 Type II theory 344
22.4 World sheet supersymmetry 345
22.5 The spectra of the superstrings 346
22.6 Manifest space-time supersymmetry: the
Green–Schwarz formalism 353
22.7 Vertex operators 355
Suggested reading 356
Exercises 356
23 The heterotic string 359
23.1 The O(32) theory 360
23.2 The E8 × E8 theory 361
23.3 Heterotic string interactions 361
23.4 A non-supersymmetric heterotic string theory 363
Suggested reading 363
Exercises 364
24 Effective actions in ten dimensions 365
24.1 Coupling constants in string theory 368
Suggested reading 371
Exercise 371
25 Compactification of string theory I. Tori and orbifolds 373
25.1 Compactification in field theory: the Kaluza–Klein program 373
25.2 Closed strings on tori 377
25.3 Enhanced symmetries 380
25.4 Strings in background fields 382
25.5 Bosonic formulation of the heterotic string 386
25.6 Orbifolds 387
25.7 Effective actions in four dimensions for orbifold models 395
25.8 Non-supersymmetric compactifications 398
Suggested reading 399
Exercises 400
26 Compactification of string theory II. Calabi–Yau compactifications 401
26.1 Mathematical preliminaries 401
26.2 Calabi–Yau spaces: constructions 406
26.3 The spectrum of Calabi–Yau compactifications 409
26.4 World sheet description of Calabi–Yau compactification 411
26.5 An example: the quintic in CP4 414
26.6 Calabi–Yau compactification of the heterotic
string at weak coupling 416
Suggested reading 426
Exercises 427
27 Dynamics of string theory at weak coupling 429
27.1 Non-renormalization theorems 430
27.2 Fayet–Iliopoulos D-terms 434
27.3 Gaugino condensation 438
27.4 Obstacles to a weakly coupled string phenomenology 439
Suggested reading 440
28 Beyond weak coupling: non-perturbative string theory 441
28.1 Perturbative dualities 442
28.2 Strings at strong coupling: duality 442
28.3 D-branes 443
28.4 Branes from T-duality of Type I strings 447
28.5 Strong–weak coupling dualities: the equivalence of
different string theories 451
28.6 Strong–weak coupling dualities: some evidence 452
28.7 Strongly coupled heterotic string 458
28.8 Non-perturbative formulations of string theory 460
Suggested reading 465
Exercises 466
29 Large and warped extra dimensions 467
29.1 Large extra dimensions: the ADD proposal 467
29.2 Warped spaces: the Randall–Sundrum proposal 470
Suggested reading 473
Exercise 473
30 Coda: where are we headed? 475
Suggested reading 479
Part 4 The appendices 481
Appendix A Two-component spinors 483
Appendix B Goldstone’s theorem and the pi mesons 487
Exercises 489
Appendix C Some practice with the path integral in field theory 491
C.1 Path integral review 491
C.2 Finite-temperature field theory 492
C.3 QCD at high temperature 495
C.4 Weak interactions at high temperature 496
C.5 Electroweak baryon number violation 497
Suggested reading 499
Exercises 499
Appendix D The beta function in supersymmetric Yang–Mills theory 501
Exercise 503
References 505
Index 511