Supersymmetric Solitons

Half-title......Page 3
Series-title......Page 4
Title......Page 7
Copyright......Page 8
Contents......Page 11
Acknowledgments......Page 15
Abbreviations......Page 16
1 Introduction......Page 17
Part I Short excursion......Page 21
2.1 History......Page 23
2.2 Minimal supersymmetry......Page 24
2.2.2 D = 3......Page 25
2.2.3 D = 4......Page 26
2.3.1 N = 2 in D = 2......Page 27
2.3.2 N = 2 in D = 3......Page 28
2.3.3 On extended supersymmetry (eight supercharges) in D = 4......Page 29
3.1.1 Preliminaries......Page 31
3.1.2 Domain wall in the minimal Wess–Zumino model......Page 34
3.1.3 D-branes in gauge field theory......Page 40
3.1.4 Domain wall junctions......Page 45
3.1.5 Webs of walls......Page 47
3.2 Vortices in = 3 and flux tubes in = 4......Page 48
3.2.1 SQED in 3D......Page 49
3.2.2 Four-dimensional SQED and the ANO string......Page 56
3.2.3 Flux tube junctions......Page 57
3.3.1 The Georgi–Glashow model: vacuum and elementary excitations......Page 59
3.3.3 Mass and magnetic charge......Page 61
3.3.4 Solution of the Bogomol'nyi equation for monopoles......Page 63
3.3.5 Collective coordinates (moduli)......Page 65
3.3.6 Singular gauge, or how to comb a hedgehog......Page 70
3.3.7 Monopoles in SU(N)......Page 71
3.3.8 The term induces a fractional electric charge for the monopole (the Witten effect)......Page 75
3.4 Monopoles and fermions......Page 76
3.4.1 N = 2 super-Yang–Mills (without matter)......Page 77
3.4.2 Supercurrents and the monopole central charge......Page 78
3.4.3 Zero modes for adjoint fermions......Page 81
3.4.4 Zero modes for fermions in the fundamental representation......Page 82
3.5 More on kinks (in N = 2 CP(1) model)......Page 83
3.5.1 BPS solitons at the classical level......Page 85
3.5.2 Quantization of the bosonic moduli......Page 87
3.5.3 The kink mass and holomorphy......Page 88
3.5.4 Fermions in quasiclassical consideration......Page 90
3.5.5 Combining bosonic and fermionic moduli......Page 92
Part II Long journey......Page 95
Warning......Page 96
Introduction to Part II......Page 97
4.1 Basic model: N = 2 SQCD......Page 101
4.1.1 SU(N)×U(1) N = 2 QCD......Page 104
4.1.2 The vacuum structure and excitation spectrum......Page 105
4.2 Abelian strings......Page 108
4.3 Elementary non-Abelian strings......Page 114
4.4 The world-sheet effective theory......Page 115
4.4.1 Derivation of the CP(N – 1) model......Page 116
4.4.2 Fermion zero modes......Page 120
4.4.3 Physics of the CP(N – 1) model with N = 2......Page 124
4.4.4 Unequal quark masses......Page 126
4.5 Confined monopoles as kinks of the CP(N – 1) model......Page 131
4.5.1 The first-order master equations......Page 134
4.5.2 The string junction solution in the quasiclassical regime......Page 136
4.5.3 The strong coupling limit......Page 139
4.6 Two-dimensional kink and four-dimensional Seiberg–Witten solution......Page 142
4.7 More quark flavors......Page 146
4.8 Non-Abelian k-strings......Page 151
4.9 A physical picture of the monopole confinement......Page 153
5 Less supersymmetry......Page 158
5.1.1 Deformed theory and string solutions......Page 160
5.1.2 Heterotic CP(N – 1) model......Page 165
5.1.3 Large-N solution......Page 169
5.1.4 Limits of applicability......Page 173
5.2 The M model......Page 175
5.3 Confined non-Abelian monopoles......Page 179
5.4 Index theorem......Page 182
6.1 Non-Abelian strings in non-supersymmetric theories......Page 187
6.1.1 World-sheet theory......Page 188
6.1.2 Physics in the large-N limit......Page 190
The Higgs phase......Page 191
The Coulomb/confining phase......Page 192
6.2 Non-Abelian strings in N = 1*theory
......Page 198
7 Strings on the Higgs branches......Page 204
7.1 Extreme type-I strings......Page 205
7.2 Example: N = 1 SQED with the FI term......Page 208
8 Domain walls as D-brane prototypes......Page 212
8.1 N = 2 supersymmetric QED......Page 213
8.2 Domain walls in N = 2 SQED......Page 215
8.3 Effective field theory on the wall......Page 218
8.4 Domain walls in the U(N) gauge theories......Page 222
9.1 Strings ending on the wall......Page 225
9.2 Boojum energy......Page 228
9.3 Finite-size rigid strings stretched between the walls. Quantizing string endpoints......Page 230
9.4 Quantum boojums. Physics of the world volume theory......Page 235
10 Conclusions......Page 239
A.2 Covariant derivatives......Page 244
A.3 Superspace and superfields......Page 245
A.7 Euclidean notation......Page 247
A.8 Group-theory coefficients......Page 248
A.9 Renormalization-group conventions......Page 249
B.1 O(3) sigma model......Page 250
B.2 CP(1) sigma model......Page 251
B.3 Geometric interpretation......Page 253
B.4 Gauged formulation......Page 254
B.5 Heterotic CP(1)......Page 256
C.1 N = 2 supersymmetric QED......Page 259
C.2 String solutions......Page 260
C.3 The fermion zero modes......Page 263
References......Page 264
Index......Page 272
Author index......Page 274