Preface ........................................................ xv
1 A Brief History of Unification ............................... 1
References .................................................. 17
2 Gravitation ................................................. 20
2.1 The Equivalence Principle .............................. 20
2.2 The Ricci Tensor and Curvature Scalar .................. 30
2.3 The Einstein Field Equations ........................... 31
2.4 Variation of the Einstein Action ....................... 31
2.5 The Stress Tensor ...................................... 32
2.6 The Linearized Field Equations of Einstein Gravity ..... 34
2.7 Motion of a Particle in a Non-inertial Frame ........... 35
2.8 The Newtonian Limit .................................... 36
2.9 Gauge Transformations of the Einstein Metric ........... 39
2.10 The Palatini Variational Method ........................ 40
2.11 The Vierbein Formalism ................................. 41
2.12 Modifications of the Einstein Theory ................... 45
2.13 Parallel Transport ..................................... 45
2.14 Problems ............................................... 47
References .................................................. 50
Further Reading ............................................. 51
3 Non-abelian Gauge Theory .................................... 52
3.1 Yang-Mills Gauge Theory ................................ 52
3.2 Canonical Quantization of the Maxwell Theory ........... 55
3.3 Canonical Quantization of the Yang-Mills Theory ........ 57
3.4 Gribov Ambiguity ....................................... 59
3.5 Path Integral Quantization of Yang-Mills Theory ........ 62
3.6 BRST Transformations ................................... 66
3.7 Quantum Yang-Mills Theory .............................. 68
3.8 Problems ............................................... 69
References .................................................. 71
Further Reading ............................................. 71
4 Spontaneous Breaking of Global and Local Symmetries ......... 72
4.1 Spontaneous Breaking of Abelian Symmetries ............. 72
4.2 Spontaneous Breaking of Non-abelian Symmetries ......... 75
4.3 Problems ............................................... 78
References .................................................. 78
5 The Standard Model .......................................... 79
5.1 Electroweak Sector of the Standard Model ............... 79
5.2 The Strong Interaction Sector of the Standard Model .... 86
5.3 Problems ............................................... 87
References .................................................. 89
Further Reading ............................................. 89
6 Anomalies ................................................... 90
6.1 Introduction ........................................... 90
6.2 The Path Integral Approach ............................. 92
6.3 The Wess-Zumino Consistency Conditions ................. 96
6.4 The BRST Approach and the Wess-Zumino Consistency
Conditions ............................................. 97
6.5 Application of Consistency Conditions to Determine
Anomalies .............................................. 99
6.6 Mixed-gauge and Gravitational and Purely Gravitational
Anomalies ............................................. 104
6.7 Anomalies and Differential Geometry ................... 105
6.8 t'Hooft Matching Conditions ........................... 107
6.9 Anomaly Constraints for Unified Models ................ 107
6.10 The Standard Model Anomalies .......................... 110
6.11 Problems .............................................. 111
References ................................................. 113
7 Effective Lagrangians ...................................... 116
7.1 The Effective Lagrangian and Current Algebra .......... 123
7.2 The Chiral U(3) × U(3) Current Algebra ................ 126
7.3 The UA(1) Anomaly ..................................... 127
7.4 The θ Dependence of the Effective Lagrangian .......... 130
7.5 Appendix: The в Dependence of the UA(1) anomaly ....... 131
7.6 Problems .............................................. 136
References ................................................. 137
Further Reading ............................................ 138
8 Supersymmetry .............................................. 139
8.1 The Coleman-Mandula Theorem ........................... 139
8.2 Graded Lie Algebras ................................... 140
8.3 Two-component Spinors ................................. 142
8.4 Left Chiral Superfields ............................... 145
8.5 Right Chiral Superfields .............................. 148
8.6 Products of Chiral Superfields ........................ 149
8.7 Products of Chiral Left and Chiral Right Superfields .. 151
8.8 Construction of Supersymmetric Action Using
Superfields ........................................... 152
8.9 Vector Superfields .................................... 155
8.10 Vector Field Strength ................................. 158
8.11 The Fayet-Iliopoulos D Term ........................... 161
8.12 Superfields for Non-abelian Gauge Theories ............ 161
8.13 Supersymmetric Non-abelian Gauge Field Strengths and
Lagrangians ........................................... 161
8.14 The Interaction between Matter and Gauge Fields ....... 166
8.15 Supersymmetry Breaking ................................ 168
8.16 F-type Breaking of Supersymmetry ...................... 170
8.17 D-type Breaking of Supersymmetry ...................... 172
8.18 Spurion Fields ........................................ 176
8.19 R-Symmetry ............................................ 177
8.20 Linear Multiplets ..................................... 179
8.21 Problems .............................................. 180
References ................................................. 182
Further Reading ............................................ 183
9 Grand Unification .......................................... 184
9.1 SU(4)  SU(2)L SU(2)R Unification ................... 184
9.2 SU(5) Grand Unification ............................... 186
9.3 Supersymmetric Grand Unification ...................... 196
9.4 SO(10) Grand Unification .............................. 201
9.5 Unification with Exceptional Groups ................... 219
9.6 Quark-Lepton Masses ................................... 220
9.7 Vector Multiplets ..................................... 223
9.8 Appendix .............................................. 224
9.9 Problems .............................................. 230
References ................................................. 233
Further Reading ............................................ 235
10 The MSSM Lagrangian ........................................ 236
10.1 The Scalar Potential .................................. 240
10.2 The Fermion Sector .................................... 241
10.3 Gaugino-Higgsino Sector ............................... 242
References ................................................. 246
Further Reading ............................................ 246
11 N = 1 Supergravity ......................................... 247
11.1 Supergravity with Auxiliary Fields .................... 250
11.2 Tensor Calculus for Scalar and Vector Multiplets in
Supergravity .......................................... 252
References ................................................. 255
12 Coupling of Supergravity with Matter and Gauge Fields ...... 257
12.1 Problems .............................................. 261
References ................................................. 261
13 Supergravity Grand Unification ............................. 262
13.1 Spontaneous Breaking of Gauge Symmetry ................ 263
13.2 Spontaneous Breaking of Supersymmetry ................. 264
13.3 Mass Matrices ......................................... 265
13.4 Generation of Soft Terms in Supergravity Models ....... 267
13.5 Problems .............................................. 272
References ................................................. 272
14 Phenomenology of Supergravity Grand Unification ............ 274
14.1 Radiative Breaking of SU(2)L × U(1)Y ................... 277
14.2 The Super-GIM Mechanism ............................... 284
14.3 Higgs Bosons .......................................... 285
14.4 Loop Corrections to the Higgs Boson Mass .............. 286
14.5 Low-Energy Higgs Theorems ............................. 287
14.6 Diphoton Decay of the Higgs Boson ..................... 289
14.7 Hyperbolic Geometry: The Focus Point, Focal Curves,
and Focal Surfaces .................................... 290
14.8 Non-universalities in Soft Breaking ................... 292
14.9 Yukawa Unification .................................... 293
14.10 Supersymmetry at the Large Hadron CoUider ............ 295
14.11 Problems ............................................. 298
References ................................................. 299
Further Reading ............................................ 303
15 CP Violation in Supergravity Unified Theories .............. 304
15.1 Introduction .......................................... 304
15.2 Violation of CP in the Standard Model ................. 305
15.3 Evidence for CP Violation ............................. 306
15.4 CP Violation in Supersymmetric Theories ............... 310
15.5 The EDM of an Elementary Dirac Fermion ................ 313
15.6 The EDM of a Charged Lepton in Supersymmetry .......... 314
15.7 The EDM of Quarks ..................................... 315
15.8 The EDM Operator Contribution to the EDM of Quarks .... 315
15.9 Contribution of the Chromoelectric Dipole Moment
to the EDM of the Quarks .............................. 316
15.10 The EDM of the Quarks from the Purely Gluonic
Dimension 6 Operator ................................. 317
15.11 g-2 with Phases ...................................... 319
15.12 Supersymmetry CP Phases and CP-Even-CP-Odd
Mixing in the Neutral Higgs Boson Sector ............. 324
15.13 Effect of CP Phases on Neutralino Dark Matter ........ 328
15.14 Appendix: Renormalization Group Evolution of the
EDM .................................................. 330
15.15 Problems ............................................. 332
References ................................................. 332
16 Proton Stability in Supergravity Unified Theories .......... 335
16.1 Proton Decay from Lepto-quarks ........................ 337
16.2 Proton Decay in Supersymmetric Theories ............... 340
16.3 Effective Lagrangian for Nucleon Decay ................ 345
16.4 Problems .............................................. 349
References ................................................. 350
17 Cosmology, Astroparticle Physics, and Supergravity
Unification ................................................ 353
17.1 Particle Properties in the Early Universe ............. 357
17.2 Time and Temperature .................................. 363
17.3 Supersymmetry and Dark Matter ......................... 363
17.4 Inflation ............................................. 372
17.5 Baryogenesis and Leptogenesis ......................... 389
17.6 Problems .............................................. 399
References ................................................. 401
Further Reading ............................................ 403
18 Extended Supergravities and Supergravities from
Superstrings ............................................... 404
18.1 Supergravity in Higher Dimensions ..................... 405
18.2 Supergravities from Superstrings ...................... 409
18.3 Four-Dimensional String Models ........................ 421
18.4 Gravitino Decay ....................................... 423
18.5 Problems .............................................. 424
References ................................................. 425
Further Reading ............................................ 427
19 Specialized Topics ......................................... 428
19.1 Models with Extra Dimensions .......................... 428
19.2 Gravity in Extra Dimensions ........................... 432
19.3 Stueckelberg Mechanism in Supergravity and in
Strings ............................................... 432
19.4 Stueckelberg Extension of the Standard Model .......... 435
19.5 Supersymmetric Extension of the Stueckelberg Model .... 438
19.6 Kinetic Mixing ........................................ 439
19.7 Problems .............................................. 441
References ................................................. 441
20 The Future of Unification .................................. 443
21 Appendices ................................................. 446
21.1 Exterior Differential Forms ........................... 446
21.2 Two-component Notation ................................ 450
21.3 Grassmann Co-ordinates ................................ 451
21.4 Geometry on Supermanifolds ............................ 456
21.5 Group Theory .......................................... 464
21.6 Couplings of N = 1 Supergravity with Matter and
Gauge Fields .......................................... 477
21.7 Further Details on the Couplings of the MSSM/
Supergravity Lagrangian ............................... 484
Further Reading ....................................... 488
22 Notation, Conventions, and Formulae ........................ 489
22.1 Lagrangians ........................................... 489
22.2 U(3) Matrices ......................................... 491
22.3 The Standard Model Relations .......................... 492
22.4 MSSM Fields and Quantum Numbers ....................... 493
22.5 SU(5) ................................................. 493
22.6 The Fierz Rearrangement ............................... 494
22.7 Dimensional Regularization ............................ 495
Further Reading ............................................ 498
23 Constants and Units ........................................ 499
23.1 Physical Constants .................................... 499
23.2 Natural Units ......................................... 500
23.3 Astrophysical Parameters .............................. 501
23.4 Cross-section Units ................................... 501
23.5 Numerical Constants ................................... 501
24 Further Reading ......................................... 502
24.1 Field Theory and Gauge Theories ....................... 502
24.2 Supersymmetry and Supergravity ........................ 502
24.3 Relativity ............................................ 504
24.4 Cosmology ............................................. 504
24.5 Other Recommended Publications ........................ 504
Author Index .................................................. 506
Subject Index ................................................. 515
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