Supergravity:
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| Main Authors: | , |
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| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2012
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| Edition: | 1. publ. |
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| Physical Description: | XVII, 607 S. |
| ISBN: | 9780521194013 |
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| 084 | |a PHY 045f |2 stub | ||
| 100 | 1 | |a Freedman, Daniel Z. |d 1939- |e Verfasser |0 (DE-588)1022607006 |4 aut | |
| 245 | 1 | 0 | |a Supergravity |c Daniel Z. Freedman and Antoine Van Proeyen |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2012 | |
| 300 | |a XVII, 607 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Supergravity | |
| 650 | 7 | |a SCIENCE / Mathematical Physics |2 bisacsh | |
| 650 | 0 | 7 | |a Supersymmetrie |0 (DE-588)4128574-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Supergravitation |0 (DE-588)4184109-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Supergravitation |0 (DE-588)4184109-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Supersymmetrie |0 (DE-588)4128574-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Proeyen, Antoine van |e Verfasser |0 (DE-588)1022607189 |4 aut | |
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Contents
Preface
Acknowledgements
Introduction
page
xv
xvii
Part I Relativistic field theory in Minkowski spacetime
1
Scalar field theory and its symmetries
1.1
The scalar field system
1.2
Symmetries of the system
1.2.1
ЅО(л)
internal symmetry
1.2.2
General internal symmetry
1.2.3
Spacetime symmetries
-
the
Lorentz
and
Poincaré
groups
1.3
Noether currents and charges
1.4
Symmetries in the canonical formalism
1.5
Quantum operators
1.6
The
Lorentz
group for
D
— 4
The Dirac field
2.1
The homomorphism of SL(2.
2.3
2.4
2.5
2.6
2.7
) ->
SO(3.
1)
The Dirac equation
Dirac adjoint and bilinear form
Dirac action
The spinors nip. s) and v(p. s) for
D
= 4
Weyl spinor fields in even spacetime dimension
Conserved currents
2.7.1
Conserved U(
1 )
current
2.7.2
Energy-momentum tensors for the Dirac field
3
Clifford algebras and spinors
3.1
The Clifford algebra in general dimension
3.1.1
The generating y-matrices
3.1.2
The complete Clifford algebra
3.1.3
Levi-Civita symbol
3.1.4
Practical y-matrix manipulation
3.1.5
Basis of the algebra for even dimension
D
=
2m
1
1
8
9
10
12
18
21
22
24
25
25
28
31
32
33
35
36
36
37
39
39
39
40
41
42
43
Contents
3.1.6
The highest rank Clifford algebra element
44
3.1.7
Odd spacetime dimension
D
=
2m
+ 1 46
3.1.8
Symmetries of y-matrices
47
3.2
Spinors in general dimensions
49
3.2.1
Spinors and spinor bilinears
49
3.2.2
Spinor indices
50
3.2.3
Fierz rearrangement
52
3.2.4
Reality
54
3.3
Majorana
spinors
55
3.3.1
Definition and properties
56
3.3.2
Symplectic
Majorana
spinors
58
3.3.3
Dimensions of minimal spinors
58
3.4
Majorana
spinors in physical theories
59
3.4.1
Variation of
a Majorana Lagrangian
59
3.4.2
Relation of
Majorana
and Weyl spinor theories
60
3.4.3
U(l) symmetries of
a Majorana
field
61
Appendix
ЗА
Details of the Clifford algebras for
D
=
2m
62
ЗА.
1
Traces and the basis of the Clifford algebra
62
ЗА.
2
Uniqueness of the
у
-matrix representation
63
3A.3 The Clifford algebra for odd spacetime dimensions
65
ЗА.
4
Determination of symmetries of y-matrices
65
ЗА.
5
Friendly representations
66
4
The Maxwell and Yang-Mills gauge fields
68
4.1
The abelian gauge field
Αμ (χ)
69
4.1.1
Gauge
invariance
and fields with electric charge
69
4.1.2
The free gauge field
71
4.1.3
Sources and Green's function
73
4.1.4
Quantum electrodynamics
76
4.1.5
The stress tensor and gauge covariant translations
77
4.2
Electromagnetic duality
77
4.2.1
Dual tensors
78
4.2.2
Duality for one free electromagnetic field
78
4.2.3
Duality for gauge field and complex scalar
80
4.2.4
Electromagnetic duality for coupled Maxwell fields
83
4.3
Non-abelian gauge symmetry
86
4.3.1
Global internal symmetry
86
4.3.2
Gauging the symmetry
88
4.3.3
Yang-Mills field strength and action
89
4.3.4
Yang-Mills theory for
G
=
SU(tV)
90
4.4
Internal symmetry for
Majorana
spinors
93
5
The free Rarita-Schwinger field
95
5.1
The initial value problem
97
Contents
5.2
Sources
and Green's function
99
5.3
Massive gravitinos from dimensional reduction
102
5.3.1
Dimensional reduction for scalar fields
102
5.3.2
Dimensional reduction for spinor fields
103
5.3.3
Dimensional reduction for the vector gauge field
104
5.3.4
Finally
4>μ(χ,γ)
104
6
Я
=
\ global supersymmetry in
D
= 4 107
6.1
Basic SUSY field theory
109
6.1.1
Conserved supercurrents
109
6.1.2
SUSY Yang-Mills theory
110
6.1.3
SUSY transformation rules
1
11
6.2
SUSY field theories of the chiral
multiplet
112
6.2.1
U(l)« symmetry
115
6.2.2
The SUSY algebra
116
6.2.3
More chiral
multiplets
119
6.3
SUSY gauge theories
120
6.3.1
SUSY Yang-Mills vector
multiplet
121
6.3.2
Chiral
multiplets
in SUSY gauge theories
122
6.4
Massless representations of
Л^
-extended
supersymmetry
125
6.4.1
Particle representations of AT-extended supersymmetry
125
6.4.2
Structure of massless representations
127
Appendix 6A Extended supersymmetry and Weyl spinors
129
Appendix 6B On- and off-shell
multiplets
and degrees of freedom
130
Partii
Differential geometry and gravity
133
7
Differential geometry
135
7.1
Manifolds
135
7.2
Scalars, vectors, tensors, etc.
137
7.3
The algebra and calculus of differential forms
140
7.4
The metric and frame field on a manifold
142
7.4.1
The metric
142
7.4.2
The frame field
143
7.4.3
Induced metrics
145
7.5
Volume forms and integration
146
7.6
Hodge duality of forms
149
7.7
Stokes'theorem and electromagnetic charges
151
7.8
p-form gauge fields
152
7.9
Connections and covariant derivatives
154
7.9.1
The first structure equation and the spin connection
ωμα/,
155
7.9.2
The
affine
connection
Γμ,,
158
7.9.3
Partial integration
160
7.10
The second structure equation and the curvature tensor
161
VII
Contents
7.11 The nonlinear
σ
-model
163
7.12
Symmetries and Killing vectors
166
7.12.1
σ
-model symmetries
166
7.12.2
Symmetries of the
Poincaré
plane
169
8
The first and second order formulations of general relativity
171
8.1
Second order formalism for gravity and bosonic matter
172
8.2
Gravitational fluctuations of flat spacetime
174
8.2.1
The graviton Green's function
177
8.3
Second order formalism for gravity and
fermions
178
8.4
First order formalism for gravity and
fermions
182
Partili
Basicsupergravity
185
9
Λ'
= 1
pure supergravity in four dimensions
187
9.1
The universal part of supergravity
188
9.2
Supergravity in the first order formalism
191
9.3
The
1.5
order formalism
193
9.4
Local supersymmetry of
AÍ
= 1,0 = 4
supergravity
194
9.5
The algebra of local supersymmetry
197
9.6
Anti-de Sitter supergravity
199
10
D
= 11
supergravity
201
10.1
D<
11
from dimensional reduction
201
10.2
The field content of
D
= 11
supergravity
203
10.3
Construction of the action and transformation rules
203
10.4
The algebra of
D
= 11
supergravity
210
11
General gauge theory
212
11.1
Symmetries
212
11.1.1
Global symmetries
213
11.1.2
Local symmetries and gauge fields
217
11.1.3
Modified symmetry algebras
219
11.2
Covariant quantities
221
11.2.1
Covariant derivatives
222
11.2.2
Curvatures
223
11.3
Gauged spacetime translations
225
11.3.1
Gauge transformations for the
Poincaré
group
225
11.3.2
Covariant derivatives and general coordinate transformations
227
11.3.3
Covariant derivatives and curvatures in a gravity theory
230
11.3.4
Calculating transformations of covariant quantities
231
Appendix
11
A Manipulating covariant derivatives
233
11
A.
1
Proof of the main lemma
233
11
A.
2
Examples in supergravity
234
Contents
12
Survey of supergravities
236
12.1
The minimal superalgebras
236
12.1.1
Four dimensions
236
12.1.2
Minimal superalgebras in higher dimensions
237
12.2
The
/č-symmetry
group
238
12.3
Multiplets
240
12.3.1
Multiplets
in four dimensions
240
12.3.2
Multiplets
in more than four dimensions
242
12.4
Supergravity theories: towards a catalogue
244
12.4.1
The basic theories and kinetic terms
244
12.4.2
Deformations and gauged supergravities
246
12.5
Scalars and geometry
247
12.6
Solutions and preserved supersymmetries
249
12.6.1
Anti-de Sitter superalgebras
251
12.6.2
Central charges in four dimensions
252
12.6.3
'Central charges'in higher dimensions
253
Part IV Complex geometry and global SUSY
255
13
Complex manifolds
257
13.1
The local description of complex and
Kahler
manifolds
257
13.2
Mathematical structure of
Kahler
manifolds
261
13.3
The
Kahler
manifolds CP"
263
13.4
Symmetries of
Kahler
metrics
266
13.4.1
Holomorphic Killing vectors and moment maps
266
13.4.2
Algebra of holomorphic Killing vectors
268
13.4.3
The Killing vectors of CPX
269
14
General actions with
N = 1
supersymmetry
271
14.1
Multiplets
271
14.1.1
Chiral
multiplets
272
14.1.2
Real
multiplets
274
14.2
Generalized actions by
multiplet
calculus
275
14.2.1
The
superpotential
275
14.2.2
Kinetic terms for chiral
multiplets
276
14.2.3
Kinetic terms for gauge
multiplets
277
14.3 Kahler
geometry from chiral
multiplets
278
14.4
General couplings of chiral
multiplets
and gauge
multiplets
280
14.4.1
Global symmetries of the SUSY
σ
-model
281
14.4.2
Gauge and SUSY transformations for chiral
multiplets
282
14.4.3
Actions of chiral
multiplets
in a gauge theory
283
14.4.4
General kinetic action of the gauge
multiplet
286
14.4.5
Requirements for an
M
= 1
SUS Y
gauge theory
286
14.5
The physical theory
288
Contents
14.5.1 Elimination
of auxiliary fields
288
14.5.2
The scalar potential
289
14.5.3
The vacuum state and SUSY breaking
291
14.5.4
Supersymmetry breaking and the
Goldstone fermion 293
14.5.5
Mass spectra and the
supertrace
sum rule
296
14.5.6
Coda
298
Appendix 14A Superspace
298
Appendix 14B Appendix: Covariant supersymmetry transformations
302
Part V Superconformal construction of supergravity theories
305
15
Gravity as
a conformai
gauge theory
307
15.1
The strategy
308
15.2
The
conformai
algebra
309
15.3
Conformai
transformations on fields
310
15.4
The gauge fields and constraints
313
15.5
The action
315
15.6
Recapitulation
317
15.7
Homothetic Killing vectors
317
16
The
conformai
approach to pure
λί
= 1
supergravity
321
16.1
Ingredients
321
16.1.1
Superconformal algebra
321
16.1.2
Gauge fields, transformations, and curvatures
323
16.1.3
Constraints
325
16.1.4
Superconformal transformation rules of a chiral
multiplet
328
16.2
The action
331
16.2.1
Superconformal action of the chiral
multiplet
331
16.2.2
Gauge fixing
333
16.2.3
The result
334
17
Construction of the matter-coupled
λί
= 1
supergravity
337
17.1
Superconformal tensor calculus
338
17.1.1
The superconformal gauge
multiplet
338
17.1.2
The superconformal real
multiplet
339
17.1.3
Gauge transformations of superconformal chiral
multiplets
340
17.1.4
Invariant actions
342
17.2
Construction of the action
343
17.2.1
Conformai
weights
343
17.2.2
Superconformal invariant action (ungauged)
343
17.2.3
Gauged superconformal supergravity
345
17.2.4
Elimination of auxiliary fields
347
17.2.5
Partial gauge fixing
351
17.3
Projective
Kahler
manifolds
351
Contents
17.3.1
The example of
CP"
352
17.3.2
Dilatations and holomorphic homothetic Killing vectors
353
17.3.3
The
projective
parametrization
354
17.3.4
The
Kahler
cone
357
17.3.5
The projection
358
17.3.6 Kahler
transformations
359
17.3.7
Physical
fermions
363
17.3.8
Symmetries of
projective
Kahler
manifolds
364
17.3.9
Γ
-gauge and decomposition laws
365
17.3.10
An explicit example: SU(1, 1)/U(1) model
368
17.4
From
conformai
to
Poincaré supergravity
369
17.4.1
The
superpotential
370
17.4.2
The potential
371
17.4.3
Fermion terms
371
17.5
Review and preview
373
17.5.1
Projective
and
Kähler-Hodge
manifolds
374
17.5.2
Compact manifolds
375
Appendix 17A
Kähler-Hodge
manifolds
376
17A.1 Dirac quantization condition
377
17A.2
Kähler-Hodge
manifolds
378
Appendix 17B Steps in the derivation of
(17.7) 380
Part VI
Я
= 1
supergravity actions and applications
383
18
The physical tV=
1
matter-coupled supergravity
385
18.1
The physical action
386
18.2
Transformation rules
389
18.3 Furtherremarks 390
18.3.1
Engineering dimensions
390
18.3.2
Rigid or global limit
390
18.3.3
Quantum effects and global symmetries
391
19
Applications of
ЛА=
1
supergravity
392
19.1
Supersymmetry breaking and the super-BEH effect
392
19.1.1 Goldstino
and the super-BEH effect
392
19.1.2
Extension to cosmological solutions
395
19.1.3
Mass sum rules in supergravity
396
19.2
The gravity mediation scenario
397
19.2.1
The
Polónyi
model of the hidden sector
398
19.2.2
Soft SUSY breaking in the observable sector
399
19.3
No-scale models
401
19.4
Supersymmetry and anti-de Sitter space
403
19.5 Ä-symmetry
and Fayet-Iliopoulos terms
404
19.5.1
The
7?
-gauge field and transformations
405
Contents
19.5.2 Fayet-Iliopoulos
terms
406
19.5.3 An
example with
non-minimal
Kahler
potential
406
Part
VII
Extended
Λ/"
= 2
supergravity
409
20
Construction of the matter-coupled
M
= 2
supergravity
411
20.1
Global supersymmetry
412
20.1.1
Gauge
multiplets
for
D
= 6 412
20.1.2
Gauge
multiplets
for
D
= 5 413
20.1.3
Gauge
multiplets
for
D
= 4 415
20.1.4
Hypermultiplets
418
20.1.5
Gauged hypermultiplets
422
20.2
AÍ
— 2
superconformai
calculus
425
20.2.1
The
superconformai
algebra
425
20.2.2
Gauging of the
superconformai
algebra
427
20.2.3
Conformai
matter
multiplets
430
20.2.4
Superconformai
actions
432
20.2.5
Partial gauge fixing
434
20.2.6
Elimination of auxiliary fields
436
20.2.7
Complete action
439
20.2.8
D
= 5
and
D
= 6,
Λί
= 2
supergravities
440
20.3
Special geometry
440
20.3.1
The family of special manifolds
440
20.3.2
Very special real geometry
442
20.3.3
Special
Kahler
geometry
443
20.3.4 Hyper-Kähler
and
quaternionic-Kähler
manifolds
452
20.4
From
conformai
to
Poíncaré
supergravity
459
20.4.1
Kinetic terms of the bosons
459
20.4.2
Identities of special
Kahler
geometry
459
20.4.3
The potential
460
20.4.4
Physical
fermions
and other terms
460
20.4.5
Supersymmetry and gauge transformations
461
Appendix 20A SU(2) conventions and triplets
463
Appendix 20B Dimensional reduction
6 —> 5 —>■ 4 464
20B.1 Reducing from D = 6
->-
D = 5
464
20B.2 Reducing from
Û
= 5
^
D
= 4 464
Appendix 20C Definition of rigid special
Kahler
geometry
465
21
The physical
M
= 2
matter-coupled supergravity
469
21.1
The bosonic sector
469
21.1.1
The basic (ungauged)
N — 2,
Ό
—
A matter-coupled
supergravity
469
21.1.2
The gauged supergravities
471
21.2
The symplectic formulation
472
Contents
хш
21.2.1 Symplectic
definition
21.2.2
Comparison of symplectic and prepotential formulation
21.2.3
Gauge transformations and symplectic vectors
21.2.4
Physical
fermions
and duality
21.3
Action and transformation laws
21.3.1
Final action
21.3.2
Supersymmetry transformations
21.4
Applications
21.4.1
Partial supersymmetry breaking
21.4.2
Field strengths and central charges
21.4.3
Moduli spaces of Calabi-Yau manifolds
21.5
Remarks
21.5.1
Fayet-Iliopoulos terms
21.5.2
σ
-model
symmetries
21.5.3
Engineering dimensions
Part
VIII
Classical solutions and the AdS/CFT correspondence
22
Classical solutions of gravity and supergravity
22.1
Some solutions of the field equations
22.1.1
Prelude: frames and connections on spheres
22.1.2
Anti-de Sitter space
22.
22.
oo
22.
22.
.3
AdSo obtained from its embedding in KD+1
.4
22.2
22.3
22.4
22.5
22.6
22.7
22.8
Spacetime metrics with spherical symmetry
AdS-Schwarzschild spacetime
The
Reissner-Nordström
metric
A more general
Reissner-Nordström
solution
Killing spinors and
BPS
solutions
22.2.1
The integrability condition for Killing spinors
22.2.2
Commuting and anti-commuting Killing spinors
Killing spinors for anti-de Sitter space
Extremal
Reissner-Nordström
spacetimes as
BPS
solutions
The black hole attractor mechanism
22.5.1
Example of a black hole attractor
22.5.2
The attractor mechanism
-
real slow and simple
Supersymmetry of the black holes
22.6.1
Killing spinors
22.6.2
The central charge
22.6.3
The black hole potential
First order gradient flow equations
The attractor mechanism
-
fast and furious
Appendix 22A Killing spinors for pp-waves
472
474
474
475
476
476
477
479
479
480
480
482
482
482
482
485
487
487
487
489
490
496
498
499
501
503
505
505
506
508
510
511
513
517
517
519
521
522
523
525
„¡v
Contents
23
The AdS/CFT correspondence
527
23.1
The Af
= 4
SYM
theory 529
23.2
Type IIB string theory and
ЛЗ
-branes
532
23.3
The
ОЗ-Ьгапе
solution of Type IIB
supergravity
533
23.4
Kaluza-Klein analysis on AdS5
0
S5
534
23.5
Euclidean AdS and its inversion symmetry
536
23.6
Inversion and CFT correlation functions
538
23.7
The free massive scalar field in Euclidean AdS^+i
539
23.8
AdS/CFT correlators in a toy model
541
23.9
Three-point correlation functions
543
23.10
Two-point correlation functions
545
23.11
Holographic renormalization
550
23.11.1
The scalar two-point function in a CFTj
554
23.11.2
The holographic trace anomaly
555
23.12
Holographic RG flows
558
23.12.1
AAdS domain wall solutions
559
23.12.2
The holographic c-theorem
562
23.12.3
First order flow equations
563
23.13
AdS/CFT and hydrodynamics
564
Appendix A Comparison of notation
573
A.
1
Spacetime and gravity
573
A.
2
Spinor conventions
575
A.3 Components of differential forms
576
A.
4
Covariant derivatives
576
Appendix
В
Lie algebras and superalgebras
577
B.I Groups and representations
577
B.2 Lie algebras
578
B.3 Superalgebras
581
References
583
Index
602 |
| any_adam_object | 1 |
| author | Freedman, Daniel Z. 1939- Proeyen, Antoine van |
| author_GND | (DE-588)1022607006 (DE-588)1022607189 |
| author_facet | Freedman, Daniel Z. 1939- Proeyen, Antoine van |
| author_role | aut aut |
| author_sort | Freedman, Daniel Z. 1939- |
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| building | Verbundindex |
| bvnumber | BV040147134 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.S9 |
| callnumber-search | QC174.17.S9 |
| callnumber-sort | QC 3174.17 S9 |
| callnumber-subject | QC - Physics |
| classification_rvk | UH 8500 UO 1560 |
| classification_tum | PHY 045f |
| ctrlnum | (OCoLC)796076599 (DE-599)BVBBV040147134 |
| dewey-full | 530.14/23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/23 |
| dewey-search | 530.14/23 |
| dewey-sort | 3530.14 223 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040147134 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:17:03Z |
| institution | BVB |
| isbn | 9780521194013 |
| language | English |
| lccn | 2011053360 |
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| physical | XVII, 607 S. |
| publishDate | 2012 |
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| publisher | Cambridge University Press |
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| spelling | Freedman, Daniel Z. 1939- Verfasser (DE-588)1022607006 aut Supergravity Daniel Z. Freedman and Antoine Van Proeyen 1. publ. Cambridge [u.a.] Cambridge University Press 2012 XVII, 607 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Supergravity SCIENCE / Mathematical Physics bisacsh Supersymmetrie (DE-588)4128574-8 gnd rswk-swf Supergravitation (DE-588)4184109-8 gnd rswk-swf Supergravitation (DE-588)4184109-8 s DE-604 Supersymmetrie (DE-588)4128574-8 s Proeyen, Antoine van Verfasser (DE-588)1022607189 aut http://assets.cambridge.org/97805211/94013/cover/9780521194013.jpg Cover image Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025003932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Freedman, Daniel Z. 1939- Proeyen, Antoine van Supergravity Supergravity SCIENCE / Mathematical Physics bisacsh Supersymmetrie (DE-588)4128574-8 gnd Supergravitation (DE-588)4184109-8 gnd |
| subject_GND | (DE-588)4128574-8 (DE-588)4184109-8 |
| title | Supergravity |
| title_auth | Supergravity |
| title_exact_search | Supergravity |
| title_full | Supergravity Daniel Z. Freedman and Antoine Van Proeyen |
| title_fullStr | Supergravity Daniel Z. Freedman and Antoine Van Proeyen |
| title_full_unstemmed | Supergravity Daniel Z. Freedman and Antoine Van Proeyen |
| title_short | Supergravity |
| title_sort | supergravity |
| topic | Supergravity SCIENCE / Mathematical Physics bisacsh Supersymmetrie (DE-588)4128574-8 gnd Supergravitation (DE-588)4184109-8 gnd |
| topic_facet | Supergravity SCIENCE / Mathematical Physics Supersymmetrie Supergravitation |
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