N = 1 and non-supersymmetric open string theories in six and four space-time dimensions

Titlepage......Page 1
Abstract......Page 2
Contents......Page 3
List of Figures......Page 7
List of Tables......Page 9
String theory......Page 11
Quantization of classical strings......Page 12
String theory as a theory of quantum gravity......Page 17
Supersymmetric string theories......Page 20
Compactifications......Page 27
Open strings and unoriented string theories......Page 28
Chiral fermions in open string theories......Page 30
General construction of orbifolds......Page 34
Torus compactification as an orbifold......Page 39
Moduli-space of toroidal compactifications, T-duality group and symmetries......Page 42
Compactification on T², T-duality and symmetries......Page 45
 Points of enhanced symmetry in the moduli space SO(2,2,R)......Page 47
The world-sheet-parity on T²......Page 49
Toroidal orbifolds......Page 52
Space-time supersymmetric (toroidal) orbifolds......Page 54
 The asymmetric (T²Tײ)/ (Z(3)L×Z(3)R) orbifold......Page 56
Basic concepts......Page 63
S Omega-invariant closed-string spectra and Klein bottle amplitude......Page 64
Closed-string tadpoles......Page 70
Open-strings......Page 73
Chan Paton factors and gauge symmetries......Page 75
Open-strings on orbifolds......Page 77
s Omega-invariant open-string sector......Page 83
Möbius amplitude......Page 87
Orientifolds of supersymmetric strings......Page 91
Fermionic sector of the Klein bottle......Page 92
Concluding remarks......Page 94
Open Strings in Electro-Magnetic Background-Fields......Page 96
Action and boundary conditions of the open string......Page 97
Open strings with two boundaries......Page 100
Solution to linear boundary conditions for the cylinder......Page 101
World sheet momentum and Hamiltonian......Page 102
Quantization of open strings with linear boundary conditions......Page 103
Quantization of zero- and linear-modes......Page 104
Quantization of oscillator modes......Page 107
 Quantization of zero and momentum modes in toroidal compactifications......Page 109
Hilbert-space, further quantization......Page 114
The commutator [X(tau,0),X(tau,0)]......Page 115
The commutator [X(tau,pi),X(tau,pi)]......Page 119
Space-time supersymmetry of open strings in constant backgrounds......Page 121
Closed form of the Eigenvalues lambda(i) in d=4,6.......Page 122
Concluding remarks......Page 124
Introduction......Page 126
D-branes in asymmetric orbifolds......Page 128
Definition of the T-dual torus......Page 129
The hat(Z)(3) torus......Page 130
Asymmetric rotations of D-branes......Page 131
D2-branes with F-flux on T²......Page 133
D-branes in the asymmetric hat(Z)(3) orbifold......Page 136
D1-branes on T²......Page 137
Two-point function on the disc......Page 138
The OPE of vertex operators......Page 139
The commutator of the coordinates......Page 140
Asymmetric orientifolds......Page 142
 Orientifolds on the (T²×T²)/ (Z(3)L×Z(3)R) orbifold background......Page 143
Tadpole cancellation......Page 144
Concluding remarks......Page 146
Introduction......Page 148
D9-branes with magnetic fluxes......Page 151
D(9-d)-branes at angles......Page 152
Klein bottle amplitude......Page 154
Annulus amplitude......Page 155
 Compactifications to six dimensions......Page 157
Six-dimensional models......Page 158
Four dimensional models......Page 160
A 24 generation SU(5) model......Page 161
A four generation model......Page 163
(In-) Stability of purely toroidal orientifolds......Page 165
Supersymmetric brane configurations and special Lagrangian submanifolds (sLags)......Page 166
Tachyons in toroidal orientifolds......Page 168
Concluding remarks......Page 169
The  sigma Omega -Orientifold on (T²×T²×T²)/Z(4)......Page 171
Intersecting Brane Worlds on Calabi-Yau spaces......Page 172
3-cycles in the Z(4) orbifold......Page 174
Crystallographic actions......Page 175
A non-integral basis of 3-cycles......Page 176
An integral basis of 3-cycles......Page 177
O6-planes in the Z(4) orientifold......Page 180
Supersymmetric cycles......Page 181
A four generation supersymmetric Pati-Salam model......Page 185
Green-Schwarz mechanism......Page 186
Three generation supersymmetric Pati-Salam model......Page 187
Brane recombination......Page 188
D-flatness......Page 192
Gauge symmetry breaking......Page 197
Getting the Standard Model......Page 200
Adjoint Pati-Salam breaking......Page 201
Bifundamental Pati-Salam breaking......Page 203
Concluding remarks......Page 205
Conclusions......Page 208
Acknowledgments......Page 211
Transformation under SL(2,Z):......Page 212
Poisson resummation formula for lattice sums......Page 213
Conformal blocks in D=6......Page 214
 Equivalence classes of unitary symmetric and anti-symmetric matrices.......Page 216
 Spectrum and Eigenvectors of Lorentz transformations......Page 219
Orientifold planes......Page 223
Supersymmetry conditions......Page 224
Fractional boundary states......Page 225
Bibliography......Page 227