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Oxford University Press Modern Supersymmetry; Dynamics and Duality (2006)
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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 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 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 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 ix CONTENTS 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 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 /x problem 105 6.4 Exercise 106 References 106 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 /? function 123 7.8 Superconformal symmetry 125 References 130 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 9 The Affleck Dine Seiberg superpotential 145 9.1 Symmetry and holomorphy 145 9.2 Consistency of WADS : moduli space 148 9.3 Consistency of WADS: mass perturbations 150 9.4 Generating WADS from instantons 152 9.5 Generating WADS from gaugino condensation 154 9.6 Vacuum structure 155 9.7 Exercise 155 References 155 x CONTENTS 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 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 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 13 The Seiberg Witten theory 210 13.1 The Coulomb phase of N = 1 SO(N) 210 13.2 Diversion onSO( 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 Addingflavors2 References 231 xi 214 230 CONTENTS 14 Superconformal field theories 233 14.1 A-Maximization 233 14.2 The simplest chiral SOFT 234 14.3 N = 2 and Argyres-Douglas points 239 14.4 N = 4 and orbifolds 240 References 243 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 16 Anomaly and gaugino mediation 262 16.1 "Supergravity" mediation 262 16.2 SUSY breaking 265 16.3 The fj, problem 267 16.4 Slepton masses 269 16.5 Gaugino mediation 272 16.6 Exercise 273 References 273 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 AdS5 x S5 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 A Spinors and Pauli matrices 301 A.1 Conventions 301 A.2 Fierz and Pauli identities 303 A.3 Propagators 303 B Group theory 305 B.I Classical Lie groups 305 B.2 SU(2) 307 B.3 ST/(3) 307 xii CONTENTS B.4 SU(4) 308 References 309 Index 311 |
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