Supersymmetric field theories: geometric structures and dualities
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | XII, 410 S. |
| ISBN: | 9781107053816 |
Internformat
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| 245 | 1 | 0 | |a Supersymmetric field theories |b geometric structures and dualities |c Sergio Cecotti |
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| 650 | 4 | |a Supersymmetry | |
| 650 | 4 | |a Geometrical constructions | |
| 650 | 4 | |a Duality (Nuclear physics) | |
| 650 | 4 | |a Duality theory (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804153026749923328 |
|---|---|
| adam_text | SUPERSYMMETRIC FIELD THEORIES
Adopting an elegant geometrical approach, this advanced pedagogical text
describes deep and intuitive methods for understanding the subtle logic of
supersymmetry, while avoiding lengthy computations.
The book describes how complex results and formulae obtained using other
approaches can be significantly simplified when translated to a geometric setting.
Introductory chapters describe geometric structures in field theory in the general
case, while detailed later chapters address specific structures such as parallel ten-
sor fields, G-structures, and isometry groups. The relationship between structures
in supergravity and period maps of algebraic manifolds, Kodaira-Spencer theory,
modularity, and the arithmetic properties of supergravity, are also addressed.
Relevant geometric concepts are introduced and described in detail, providing
a self-contained toolkit of useful techniques, formulae and constructions. Cover-
ing all the material necessary for the application of supersymmetric field theories
to fundamental physical questions, this is an outstanding resource for graduate
students and researchers in theoretical physics.
SERGIO CECOTTI is Associate Professor at Scuola Intemazionale Superiore di
Studi Avanzati (SISSA), Trieste, Italy.
Contents
Preface xi
Notations xiii
Part I How geometric structures arise in supersymmetric
field theories 1
1 Geometrical structures in (Q)FT 3
1.1 (Gauged) rr-models 3
1.2 Adding fields of arbitrary spin 8
1.3 How strings come about 15
1.4 Gauge dualities 16
1.5 The emergence of modularity 27
1.6 More dualities 34
2 Extended supersymmetry in diverse dimensions 42
2.1 SUSY in diverse dimensions 42
2.2 A little warm-up: D — 2 48
2.3 SUSY and the topology of N4 51
2.4 Extended supersymmetry in 3D 59
2.5 The language of G-structures. Flat (Gi,G2)-structures 67
2.6 Local extended supersymmetry in 3D 69
2.7 Connections with algebraic geometry 78
2.8 Supersymmetry in D — 4 and 6 dimensions 79
2.9 4D SUSY gauge theories. Special Kahler geometry 82
2.10 4D supergravity 92
Part II Geometry and extended SUSY: more than eight supercharges 101
3 Parallel structures and holonomy 103
3.1 The holonomy group 103
3.2 Symmetric Riemannian spaces 108
Contents
viii
3.3 Berger’s theorem 115
3.4 Parallel forms on AÍ 118
3.5 Parallel spinors and holonomy 120
3.6 G-structures and Spencer cohomology 123
3.7 The holonomy groups of Lorentzian manifolds 125
4 SUSY/SUGRA Lagrangians and [/-duality 129
4.1 Determination of the scalar manifold M. 129
4.2 Dimensional reduction and totally geodesic submanifolds 138
4.3 Four-fermion couplings vs. holonomy 139
4.4 Vector couplings in 4D SUGRA 143
4.5 The gauge point of view 146
4.6 The complete 4D Lagrangian: [/-duality 147
4.7 [/-duality, Z-map, and Grassmannians 150
4.8 6D chiral forms 154
4.9 Arithmetics of [/-duality. Global geometry of A ! 155
5 t-Models and symmetric spaces 160
5.1 Cartan connections on G 160
5.2 Maurier-Cartan forms 164
5.3 Invariant metrics on a compact group 166
5.4 Chiral models 168
5.5 Geometry of coset spaces G/H 169
5.6 Symmetric spaces 171
5.7 Classification of symmetric manifolds 174
5.8 Totally geodesic submanifolds. Rank 177
5.9 Other techniques 178
5.10 An example: Ej(y)/SU(8) 178
5.11 Symmetric and Iwasawa gauges 182
6 Killing spinors and rigid SUSY in curved spaces 185
6.1 Review: space-time charges in General Relativity 185
6.2 AdS space 187
6.3 Killing spinors 189
6.4 The geometry of Killing spinors 198
6.5 Nester form of the space-time charges 205
6.6 The AdS/Poincaré SUSY algebra 207
6.7 Positive mass and BPS bounds 211
6.8 SUGRA Ward identities 214
Contents ix
7 Parallel structures and isometries 220
7.1 Rigid SUSY: momentum maps 220
7.2 Г-tensors I 227
7.3 Target space isometries in supergravity 230
7.4 Holonomy vs. isometries 231
7.5 The rigid case revisited. Superconformai geometries 236
7.6 The Cartan-Kostant isomorphism 240
7.7 The covariant momentum map 243
7.8 Г-tensors II. Generalized T in SUGRA 246
8 Gauging and potential terms 248
8.1 Gaugings in rigid SUSY 248
8.2 A-extended (rigid) CS gauge theories 250
8.3 Example: N — 4and the Gaiotto-Witten theorem 258
8.4 A puzzle and its resolution 261
8.5 World-volume theory of М2 branes: the ABJM model 265
8.6 Gauged supergravities 266
8.7 Symmetric target spaces 274
8.8 Gauged supergravity in D 4 280
8.9 An example: TV = 3 supergravity in 4D 286
8.10 Gauging maximal supergravity in Ddimensions 287
Part III Special geometries 291
9 Kàhler and Hodge manifolds 293
9.1 Complex manifolds 293
9.2 Kâhler metrics and manifolds 300
9.3 U(n)manifolds 304
9.4 Hodge theory in Kàhler spaces 305
9.5 Hodge manifolds 312
9.6 Symmetric and homogeneous Kâhler manifolds 314
10 N = 1 supergravity in 4D 321
10.1 A/՜ = 2 supergravity in 3D 321
10.2 A/՜ = 1 D = 4 ungauged supergravity 325
10.3 SuperHiggs. Flat potentials 327
10.4 Gauged N = 1 4D supergravity 331
11 Flag manifolds. Variations of Hodge structures 335
11.1 Hodge structures and Griffiths domains 335
11.2 Geometry of reductive homogeneous spaces G/V 341
11.3 Quick review of Kodaira-Spencer theory 345
X
Contents
11.4 Variations of Hodge structures (VHS) 348
11.5 The case of a Calabi-Yau 3-fold 358
12 Four-dimensional N = 2 supergravity 368
12.1 The four geometric structures oïM — 2 supergravity 368
12.2 K D V n Z, or projective special Kåhler geometry 369
12.3 Formulas in projective special coordinates 371
12.4 Aspects of projective special Kåhler manifolds 376
12.5 Coupling hypermultiplets to N = 2 supergravity 380
12.6 Compactifying type II supergravity on a CY manifold 382
12.7 Hypermultiplets: the c-map 387
Appendix G— structures on manifolds 390
References 394
Index 408
|
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| author_role | aut |
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| classification_rvk | UO 1560 UO 4000 |
| ctrlnum | (OCoLC)899761462 (DE-599)BSZ423710893 |
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| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.725 |
| dewey-search | 539.725 |
| dewey-sort | 3539.725 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| isbn | 9781107053816 |
| language | English |
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| spelling | Cecotti, Sergio Verfasser aut Supersymmetric field theories geometric structures and dualities Sergio Cecotti 1. publ. Cambridge Cambridge Univ. Press 2015 XII, 410 S. txt rdacontent n rdamedia nc rdacarrier Supersymmetry Geometrical constructions Duality (Nuclear physics) Duality theory (Mathematics) Feldtheorie (DE-588)4016698-3 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Supersymmetrie (DE-588)4128574-8 gnd rswk-swf Supersymmetrie (DE-588)4128574-8 s Feldtheorie (DE-588)4016698-3 s Dualität (DE-588)4013161-0 s SWB Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818920&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818920&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cecotti, Sergio Supersymmetric field theories geometric structures and dualities Supersymmetry Geometrical constructions Duality (Nuclear physics) Duality theory (Mathematics) Feldtheorie (DE-588)4016698-3 gnd Dualität (DE-588)4013161-0 gnd Supersymmetrie (DE-588)4128574-8 gnd |
| subject_GND | (DE-588)4016698-3 (DE-588)4013161-0 (DE-588)4128574-8 |
| title | Supersymmetric field theories geometric structures and dualities |
| title_auth | Supersymmetric field theories geometric structures and dualities |
| title_exact_search | Supersymmetric field theories geometric structures and dualities |
| title_full | Supersymmetric field theories geometric structures and dualities Sergio Cecotti |
| title_fullStr | Supersymmetric field theories geometric structures and dualities Sergio Cecotti |
| title_full_unstemmed | Supersymmetric field theories geometric structures and dualities Sergio Cecotti |
| title_short | Supersymmetric field theories |
| title_sort | supersymmetric field theories geometric structures and dualities |
| title_sub | geometric structures and dualities |
| topic | Supersymmetry Geometrical constructions Duality (Nuclear physics) Duality theory (Mathematics) Feldtheorie (DE-588)4016698-3 gnd Dualität (DE-588)4013161-0 gnd Supersymmetrie (DE-588)4128574-8 gnd |
| topic_facet | Supersymmetry Geometrical constructions Duality (Nuclear physics) Duality theory (Mathematics) Feldtheorie Dualität Supersymmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818920&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818920&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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