S. James Gates0805331611, 9780805331615, 0805331603
Table of contents :
Preface……Page 3
1. INTRODUCTION……Page 7
2. A TOY SUPERSPACE……Page 13
a. Index conventions……Page 15
b. Superspace……Page 16
a. Representations……Page 17
b. Components by expansion……Page 18
c. Actions and components by projection……Page 19
d. Irreducible representations……Page 21
2.3. Scalar multiplet……Page 23
a. Abelian gauge theory……Page 26
b. Nonabelian case……Page 32
c. Gauge invariant masses……Page 34
a. Superforms: general case……Page 36
b. Super 2-form……Page 38
c. Spinor gauge superfield……Page 40
a. Supercoordinate transformations……Page 42
c. Covariant derivatives……Page 43
d. Gauge choices……Page 45
e. Field strengths……Page 46
f. Bianchi identities……Page 47
g. Actions……Page 50
a. Scalar multiplet……Page 54
b. Vector multiplet……Page 60
3. REPRESENTATIONS OF SUPERSYMMETRY……Page 62
a. Index conventions……Page 64
c. Symmetrization and antisymmetrization……Page 66
d. Conjugation……Page 67
e. Levi-Civita tensors and index contractions……Page 68
a. Lie algebras……Page 72
c. Super-Poincare algebra……Page 73
d. Positivity of the energy……Page 74
e. Superconformal algebra……Page 75
f. Super-deSitter algebra……Page 77
a. Particle representations……Page 79
b. Representations on superfields……Page 84
a. Construction……Page 93
b. Algebraic relations……Page 94
c. Geometry of flat superspace……Page 96
d. Casimir operators……Page 97
3.5. Constrained superfields……Page 99
a. theta-expansions……Page 102
b. Projection……Page 104
c. The transformation superfield……Page 106
a. Berezin integral……Page 107
c. Superdeterminants……Page 109
a. Differentiation……Page 111
b. Integration……Page 113
3.9. Physical, auxiliary, and gauge components……Page 118
a. Stueckelberg formalism……Page 122
b. CP1 model……Page 123
c. Coset spaces……Page 127
a. General……Page 130
b. Examples……Page 138
a. Field strengths……Page 148
b. Light-cone formalism……Page 152
3.13. Off-shell field strengths and prepotentials……Page 157
4. CLASSICAL, GLOBAL, SIMPLE (N=1) SUPERFIELDS……Page 159
a. Renormalizable models……Page 161
b. Nonlinear sigma-models……Page 166
a. Prepotentials……Page 171
b. Covariant approach……Page 182
c. Bianchi identities……Page 186
a. Renormalizable models……Page 190
b. CPn models……Page 191
a. General……Page 193
b. Vector multiplet……Page 197
c. Tensor multiplet……Page 198
d. Gauge 3-form multiplets……Page 205
e. 4-form multiplet……Page 209
a. Gauge Wess-Zumino model……Page 210
b. The nonminimal scalar multiplet……Page 211
c. More variant multiplets……Page 213
d. Superfield Lagrange multipliers……Page 215
e. The gravitino matter multiplet……Page 218
a. N=2 multiplets……Page 228
b. N=4 Yang-Mills……Page 240
5. CLASSICAL N=1 SUPERGRAVITY……Page 244
a. Potentials……Page 246
b. Covariant derivatives……Page 249
c. Actions……Page 252
d. Conformal compensator……Page 254
a. Conformal……Page 258
b. Poincare……Page 269
c. Density compensators……Page 273
d. Gauge choices……Page 275
e. Summary……Page 277
f. Torsions and curvatures……Page 278
a. Choice of constraints……Page 281
b. Solution to constraints……Page 290
5.4. Solution to Bianchi identities……Page 306
a. Review of vector and chiral representations……Page 313
c. Tensor compensators……Page 314
e. Representation independent form of the chiral measure……Page 315
f. Scalar multiplet……Page 316
g. Vector multiplet……Page 320
h. General matter models……Page 321
i. Supergravity actions……Page 323
j. Field equations……Page 327
a. General considerations……Page 329
b. Wess-Zumino gauge for supergravity……Page 331
c. Commutator algebra……Page 334
d. Local supersymmetry and component gauge fields……Page 335
e. Superspace field strengths……Page 337
f. Supercovariant supergravity field strengths……Page 339
g. Tensor calculus……Page 340
h. Component actions……Page 345
5.7. DeSitter supersymmetry……Page 349
6. QUANTUM GLOBAL SUPERFIELDS……Page 351
6.1. Introduction to supergraphs……Page 353
a. Ordinary Yang-Mills theory……Page 356
b. Supersymmetric Yang-Mills theory……Page 359
c. Other gauge multiplets……Page 362
a. Derivation of Feynman rules……Page 364
b. A sample calculation……Page 369
c. The effective action……Page 373
d. Divergences……Page 374
e. D-algebra……Page 376
6.4. Examples……Page 380
a. Ordinary Yang-Mills……Page 389
b. Supersymmetric Yang-Mills……Page 393
c. Covariant Feynman rules……Page 398
d. Examples……Page 405
a. General……Page 409
b. Dimensional reduction……Page 410
c. Other methods……Page 414
6.7. Anomalies in Yang-Mills currents……Page 417
7. QUANTUM N=1 SUPERGRAVITY……Page 424
7.1. Introduction……Page 426
a. Formalism……Page 428
b. Expanding the action……Page 433
a. Ghost counting……Page 438
b. Hidden ghosts……Page 442
c. More compensators……Page 444
d. Choice of gauge parameters……Page 447
7.4. Quantization……Page 449
a. Feynman rules……Page 456
b. The transverse gauge……Page 458
c. Linearized expressions……Page 459
d. Examples……Page 461
7.6. Covariant Feynman rules……Page 464
a. N=1……Page 470
b. General N……Page 473
7.8. Examples……Page 478
7.9. Locally supersymmetric dimensional regularization……Page 487
a. Introduction……Page 491
b. Conformal anomalies……Page 492
c. Classical supercurrents……Page 498
d. Superconformal anomalies……Page 502
e. Local supersymmetry anomalies……Page 507
f. Not the Adler-Bardeen theorem……Page 513
8. BREAKDOWN……Page 514
8.1. Introduction……Page 516
8.2. Explicit breaking of global supersymmetry……Page 520
a. Renormalizable theories……Page 526
b. Nonrenormalizable theories……Page 531
c. Global gauge systems……Page 533
a. Explicit breaking……Page 538
b. Spontaneous breaking……Page 540
8.5. Nonlinear realizations……Page 542
8.6. SuperHiggs mechanism……Page 547
8.7. Supergravity and symmetry breaking……Page 549
a. Mass matrices……Page 552
b. Superfield computation of the supertrace……Page 559
c. Examples……Page 560
INDEX……Page 562
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