## Modern Supersymmetry: Dynamics and Duality

### CONTENTS

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 | |

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 mu 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 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 | |

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 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 | |

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 | |

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 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 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 | |

Appendix A Spinors and Pauli matrices | 301 | |

A.1 Conventions | 301 | |

A.2 Fierz and Pauli identities | 303 | |

A.3 Propagators | 303 | |

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 |