Preface ........................................................ xi
1 The Standard Model and beyond ................................ 1
1.1 The Standard Model of particle physics .................. 1
1.2 Grand Unified Theories .................................. 4
1.3 The SM fine-tuning puzzles ............................. 12
1.4 Extra dimensions ....................................... 18
2 Supersymmetry ............................................... 25
2.1 Four-dimensional N = l supersymmetry ................... 25
2.2 SUSY breaking .......................................... 32
2.3 N = 1 Supergravity ..................................... 35
2.4 Extended supersymmetry and supergravity ................ 37
2.5 Non-perturbative dynamics in supersymmetric theories ... 41
2.6 Low-energy supersymmetry and the MSSM .................. 44
3 Introduction to string theory: the bosonic string ........... 62
3.1 Generalities ........................................... 63
3.2 Closed bosonic string .................................. 72
3.3 Open bosonic string .................................... 91
3.4 Unoriented bosonic string theory ....................... 97
4 Superstrings ............................................... 103
4.1 Fermions on the worldsheet ............................ 103
4.2 Type II string theories ............................... 104
4.3 Heterotic string theories ............................. 117
4.4 Type I string theory .................................. 126
4.5 Summary ............................................... 134
5 Toroidal compactification of superstrings .................. 136
5.1 Type II superstrings .................................. 136
5.2 Heterotic superstrings ................................ 141
5.3 Type I toroidal compactification and D-branes ......... 146
6 Branes and string duality .................................. 155
6.1 D-branes in string theory ............................. 155
6.2 Supergravity description of non-perturbative states ... 165
6.3 Strings at strong coupling and lOd string duality ..... 168
6.4 AdS/CFT and gauge/gravity dualities ................... 178
6.5 Brane-antibrane systems and non-BPS D-branes .......... 180
7 Calabi-Yau compactification of heterotic superstrings ...... 185
7.1 A road map for string compactifications ............... 185
7.2 Generalities on Calabi-Yau compactification ........... 186
7.3 Heterotic СY compactifications: standard embedding .... 199
7.4 Heterotic CY compactifications: non-standard
embedding ............................................. 206
7.5 CY compactifications of Hof ava-Witten theory ......... 211
8 Heterotic string orbifolds and other exact CFT
constructions .............................................. 215
8.1 Toroidal orbifolds .................................... 215
8.2 Heterotic compactification on toroidal orbifolds ...... 218
8.3 Non-standard embeddings and Wilson lines .............. 235
8.4 Asymmetric orbifolds .................................. 242
8.5 The fermionic construction ............................ 246
8.6 Gepner models ......................................... 252
9 Heterotic string compactifications: effective action ....... 264
9.1 A first look at the heterotic 4d N = 1 effective
action ................................................ 264
9.2 Heterotic M-theory effective action ................... 272
9.3 Effective action of orbifold models ................... 273
9.4 Gauge couplings and Kac-Moody level ................... 280
9.5 Anomalous U(1)s and Fayet-Illiopoulos terms ........... 282
9.6 T-duality and the effective action .................... 286
9.7 Orbifold model building revisited ..................... 293
9.8 Higher Kac-Moody level models and string GUTs ......... 296
10 Type IIA orientifolds: intersecting brane worlds ........... 298
10.1 Type II on СY and orientifolding ...................... 298
10.2 Intersecting D6-branes in flat lOd space .............. 302
10.3 Compactification and an example of a toroidal model ... 306
10.4 Introducing O6-planes ................................. 314
10.5 Non-supersymmetric particle physics models ............ 320
10.6 Supersymmetric particle physics models in T6/Z2 × Z2
orientifolds .......................................... 325
10.7 Generalizations and related constructions ............. 329
11 Type IIB orientifolds ...................................... 340
11.1 Generalities of type IIB orientifold actions .......... 340
11.2 Type IIB toroidal orientifolds ........................ 341
11.3 D-branes at singularities ............................. 356
11.4 Magnetized D-brane models ............................. 370
11.5 F-theory model building ............................... 381
12 Type II compactifications: effective action ................ 396
12.1 The closed string moduli in type II orientifolds ...... 396
12.2 Kahler metrics of matter fields in toroidal
orientifolds .......................................... 404
12.3 The gauge kinetic function ............................ 408
12.4 U/(1)'s and FI terms .................................. 412
12.5 Superpotentials and Yukawa couplings in type II
orientifolds .......................................... 416
12.6 Effective action of an MSSM-like example .............. 426
12.7 Yukawa couplings in local F-theory models ............. 429
13 String instantons and effective field theory ............... 432
13.1 Instantons in field theory and string theory .......... 432
13.2 Fermion zero modes for D-brane instantons ............. 441
13.3 Phenomenological applications ......................... 446
14 Flux compatifkations and moduli stabilization .............. 455
14.1 Type IIB with 3-form fluxes ........................... 455
14.2 Fluxes in type II toroidal orientifolds ............... 467
14.3 D-branes and fluxes ................................... 475
14.4 Mirror symmetry, T-duality, and non-geometric fluxes .. 479
14.5 Fluxes in other string constructions .................. 482
15 Moduli stabilization and supersymmetry breaking in string
theory ..................................................... 483
15.1 SUSY and SUSY breaking in string compactifications .... 483
15.2 SUSY breaking and moduli fixing in heterotic models ... 485
15.3 SUSY breaking and moduli fixing in type II
orientifolds .......................................... 489
15.4 Soft terms from fluxes in type IIB orientifolds ....... 495
15.5 General parametrization of moduli/dilaton induced
SUSY breaking ......................................... 501
15.6 Modulus/dilaton dominated SUSY breaking spectra and
the LHC ............................................... 510
15.7 Other mediation mechanisms in string theory ........... 515
16 Further phenomenological properties. Strings and
cosmology .................................................. 518
16.1 Scales and unification in string theory ............... 518
16.2 Axions in string theory ............................... 528
16.3 R-parity and B/L-violation ............................ 531
16.4 Extra U(1) gauge bosons ............................... 534
16.5 Strings at the weak scale ............................. 540
16.6 Strings and cosmology ................................. 543
17 The space of string vacua .................................. 558
17.1 General properties of the massless spectrum in
string compactifications .............................. 558
17.2 The flavour landscape ................................. 566
17.3 The flux landscape .................................... 570
17.4 Outlook ............................................... 573
Appendix A Modular functions ................................. 576
Appendix В Some topological tools ............................ 579
B.l Forms and cycles: cohomology and homology ............. 579
B.2 Hodge dual ............................................ 584
B.3 Application: p-form gauge fields ...................... 585
B.4 Homotopy groups ....................................... 588
Appendix С Spectrum and charges of a semi-realistic Z3
heterotic orbifold ......................................... 589
Appendix D Computation of RR tadpoles ........................ 592
D.1 RR tadpoles in type I theory .......................... 592
D.2 Tadpoles for T6/ZN type IIB orientifolds .............. 595
Appendix E CFT toolkit ....................................... 597
E.1 Conformal symmetry and conformal fields ............... 597
E.2 Vertex operators and structure of scattering
amplitudes ............................................ 599
E.3 Kac-Moody algebras .................................... 602
E.4 N = 2 superconformal field theories ................... 604
E.5 Rational conformal field theory and simple currents ... 604
Bibliography .................................................. 608
References .................................................... 624
Index ......................................................... 657
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