1 Introduction to supersymmetry | 1 |
1.1 The unreasonable effectiveness of the Standard Model | 1 |
1.2 SUSY algebra | 4 |
1.3 SUSY representations | 8 |
1.4 Extended SUSY | 11 |
1.5 Central charges | 15 |
References | 17 |
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2 SUSY Lagrangians | 19 |
2.1 The free Wess-Zumino model | 19 |
2.2 Commutators of SUSY transformations | 21 |
2.3 The supercurrent and the SUSY algebra | 24 |
2.4 The interacting Wess-Zumino model | 26 |
2.5 SUSY Yang-Mills | 29 |
2.6 SUSY gauge theories | 30 |
2.7 Superspace | 34 |
2.8 N = 0 SUSY | 38 |
2.9 Exercises | 41 |
References | 41 |
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3 SUSY gauge theories | 43 |
3.1 Symmetries and group theory | 43 |
3.2 Renormalization group | 47 |
3.3 Quadratic divergence of the squark mass | 52 |
3.4 Flat directions (classical moduli space) | 53 |
3.5 The super Higgs mechanism | 56 |
3.6 Exercises | 60 |
References | 61 |
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4 The minimal supersymmetric standard model | 62 |
4.1 Particles, sparticles, and their interactions | 62 |
4.2 Electroweak symmetry breaking | 67 |
4.3 The sparticle spectrum | 72 |
4.4 Gauge coupling unification | 77 |
4.5 Radiative electroweak symmetry breaking | 78 |
4.6 One-loop correction to the Higgs mass | 79 |
4.7 Precision electroweak measurements | 81 |
4.8 Problems with flavor and CP | 82 |
4.9 Exercises | 86 |
References | 86 |
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5 SUSY breaking and the MSSM | 90 |
5.1 Spontaneous SUSY breaking at tree-level | 90 |
5.2 SUSY breaking scenarios | 93 |
5.3 The goldstino | 95 |
5.4 The goldstino theorem | 97 |
5.5 Exercises | 99 |
References | 99 |
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6 Gauge mediation | 101 |
6.1 Messengers of SUSY breaking | 101 |
6.2 RG calculation of soft masses | 102 |
6.3 Gauge mediation and the mu problem | 105 |
6.4 Exercise | 106 |
References | 106 |
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7 Nonperturbative results | 108 |
7.1 Monopoles | 108 |
7.2 Anomalies in the path integral | 113 |
7.3 Gauge anomalies | 117 |
7.4 't Hooft's anomaly matching | 118 |
7.5 Instantons | 119 |
7.6 Instantons in broken gauge theories | 121 |
7.7 NSVZ exact beta function | 123 |
7.8 Superconformal symmetry | 125 |
References | 130 |
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8 Holomorphy | 133 |
8.1 Non-renormalization theorems | 133 |
8.2 Wavefunction renormalization | 134 |
8.3 Integrating out | 135 |
8.4 The holomorphic gauge coupling | 136 |
8.5 Gaugino condensation | 139 |
8.6 NSVZ revisited | 141 |
8.7 Exercises | 143 |
References | 143 |
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9 The Affleck-Dine-Seiberg superpotential | 145 |
9.1 Symmetry and holomorphy | 145 |
9.2 Consistency of W_ADS : moduli space | 148 |
9.3 Consistency of W_ADS : mass perturbations | 150 |
9.4 Generating W_ADS from instantons | 152 |
9.5 Generating W_ADS from gaugino condensation | 154 |
9.6 Vacuum structure | 155 |
9.7 Exercise | 155 |
References | 155 |
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10 Seiberg duality for SUSY QCD | 157 |
10.1 Phases of gauge theories | 157 |
10.2 The moduli space for F>= N | 158 |
10.3 IR fixed points | 160 |
10.4 Duality | 162 |
10.5 Integrating out a flavor | 165 |
10.6 Consistency | 167 |
10.7 F = N : confinement with chiral symmetry breaking | 168 |
10.8 F = N : consistency checks | 171 |
10.9 F = N + 1: s-confinement | 173 |
10.10 Connection to theories with F > N + 1 | 176 |
10.11 Exercises | 179 |
References | 179 |
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11 More Seiberg duality | 182 |
11.1 The SO(N) moduli space | 182 |
11.2 Duality for SO(N) | 184 |
11.3 Some special cases | 186 |
11.4 Duality for Sp(2N) | 187 |
11.5 Why chiral gauge theories are interesting | 189 |
11.6 S-Confinement | 190 |
11.7 Deconfinement | 192 |
11.8 Exercises | 194 |
References | 194 |
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12 Dynamical SUSY breaking | 196 |
12.1 A rule of thumb for SUSY breaking | 196 |
12.2 The 3-2 model | 196 |
12.3 The SU(5) model | 199 |
12.4 SUSY breaking and deformed moduli spaces | 200 |
12.5 SUSY breaking from baryon runaways | 202 |
12.6 Direct gauge mediation | 205 |
12.7 Single sector models | 207 |
12.8 Exercise | 208 |
References | 208 |
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13 The Seiberg-Witten theory | 210 |
13.1 The Coulomb phase of N = 1 SO(N) | 210 |
13.2 Diversion on SO(3) | 214 |
13.3 The dyonic dual | 215 |
13.4 Elliptic curves | 217 |
13.5 N = 2: Seiberg-Witten | 221 |
13.6 The Seiberg-Witten curve | 225 |
13.7 Adding flavors | 230 |
References | 231 |
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14 Superconformal field theories | 233 |
14.1 A-Maximization | 233 |
14.2 The simplest chiral SCFT | 234 |
14.3 N = 2 and Argyres-Douglas points | 239 |
14.4 N = 4 and orbifolds | 240 |
References | 243 |
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15 Supergravity | 246 |
15.1 Supergravity: on-shell | 246 |
15.2 Supergravity: off-shell | 247 |
15.3 Coupling to matter | 249 |
15.4 10 and 11 dimensions | 251 |
15.5 Five dimensions | 258 |
15.6 Exercises | 259 |
References | 259 |
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16 Anomaly and gaugino mediation | 262 |
16.1 "Supergravity" mediation | 262 |
16.2 SUSY breaking | 265 |
16.3 The mu problem | 267 |
16.4 Slepton masses | 269 |
16.5 Gaugino mediation | 272 |
16.6 Exercise | 273 |
References | 273 |
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17 Introduction to the AdS/CFT correspondence | 275 |
17.1 D-brane constructions of gauge theories | 275 |
17.2 The supergravity approximation | 280 |
17.3 Spectra of CFT operators and AdS5xS5 KK modes | 285 |
17.4 Waves on AdS5 | 287 |
17.5 Nonperturbative static Coulomb potential | 289 |
17.6 Breaking SUSY: finite temperature and confinement | 290 |
17.7 The glueball mass gap | 291 |
17.8 Breaking SUSY: orbifolds | 294 |
17.9 Outlook | 296 |
References | 297 |
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Appendix A Spinors and Pauli matrices | 301 |
A.1 Conventions | 301 |
A.2 Fierz and Pauli identities | 303 |
A.3 Propagators | 303 |
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Appendix B Group theory | 305 |
B.1 Classical Lie groups | 305 |
B.2 SU(2) | 307 |
B.3 SU(3) | 307 |
B.4 SU(4) | 308 |
References | 309 |
Index | 311 |