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Quantum Non-Linear Sigma-Models : From Quantum Field Theory to Supersymmetry, Conformal Field Theory, Black Holes and Strings - Sergei V. Ketov

Quantum Non-Linear Sigma-Models

From Quantum Field Theory to Supersymmetry, Conformal Field Theory, Black Holes and Strings

Hardcover Published: 14th September 2000
ISBN: 9783540674610
Number Of Pages: 420

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The book is considered a systematic presentation of the modern quantum field theory of non-linear sigma-models. The contents is based on original papers. Geometrical properties and renormalization of a generic non-linear sigma-model are considered in detail, and illustrated by explicit multi-loop calculations in perturbation theory. Some non-perturbative results are derived for the conformally invariant non-linear sigma-model. Supersymmetric extensions are given for most contructions, with emphasis on their relation to complex geometry. Applications of non-linear sigma-models in conformal theory, gauge theory, string theory, and general relativity are given. The book addresses graduate sutdents and researchers in physics and mathematics.

Industry Reviews

"This is a very useful book describing many aspects and applications of nonlinear sigma-models. [...] One of the useful features of the book is that several chapters and sections can essentially be read independently, making this a practical reference book. However, the introductory chapters should also make it accessible to anyone with a basic knowledge of quantum field theory and supersymmetry." (Mathematical Reviews 2002b)

Introductionp. 1
Classical Structure and Renormalizationp. 5
Bosonic NLSM: Definition and Examplesp. 5
Covariant Background-Field Methodp. 10
Regularization and Quantum Ambiguitiesp. 18
NLSM Renormalization Group ß-Functionsp. 22
One-Loop Resultsp. 23
Two-Loop Resultsp. 24
Three-Loop Resultsp. 31
Buscher Duality and the Freedman-Townsend Modelp. 42
Gauging NLSM Isometriesp. 48
Skyrme NLSM of Pions and Nucleonsp. 50
Supersymmetric NLSMp. 57
N = 1 NLSM Action and Background-Field Methodp. 58
The Supersymmetric NLSM ß-Functionsp. 63
One-Loop Resultsp. 63
Two-Loop Resultsp. 64
Three-Loop Resultsp. 66
Four-Loop Resultsp. 68
NLSM on Homogeneous Spacesp. 80
Gauging NLSM Isometriesp. 83
N =1 NLSM in 4d, and Kähler Geometryp. 83
Gauging Isometries of 4d, N = 1 NLSMp. 87
NLSM and Extended Superspacep. 91
Complex Geometry and NLSMp. 93
ABC of Complex Geometryp. 94
4d, N = 2 NLSM in N = 1 Superspacep. 96
Triholomorphic Isometries of N = 2 NLSMp. 98
Gauging N = 2 NLSM Isometries in N = 1 Superspacep. 101
Special Geometry and Renormalizationp. 103
N = 2 Susy and Restricted Chiral Superfields in 4dp. 103
Dimensional Reduction and 2d, N = 4 Special NLSMp. 109
UV-Finiteness Versus Non-Renormalizabilityp. 113
NLSM in Projective Superspacep. 118
N = 2 Tensor Multiplet and Its Generalizations in 4dp. 119
Reduction to 4d, N =1 Superspace and Componentsp. 122
Quaternionic Geometry and Extended Supersymmetryp. 130
Perturbation Theory in Extended Superspacep. 138
Hyper-Kähler Metrics and Harmonic Superspacep. 141
Four-Dimensional Hyper-Kähler Metricsp. 142
Harmonic Superspacep. 150
Hyper-Kähler NLSM in HSSp. 155
Gauging N = 2 NLSM Isometries in HSSp. 161
NLSM and 2d Conformal Field Theoryp. 165
WZNW Models and Their Symmetriesp. 165
2d Conformal Invariancep. 165
AKM Symmetries and SS Constructionp. 172
WZNW Models and Topological Quantizationp. 176
Super-WZNW Models and Their Symmetriesp. 180
Superconformal and Super-AKM Algebrasp. 181
N = 1 and N = 2 Supersymmetric WZNW Modelsp. 186
Coset Construction and Gauged WZNW Modelsp. 194
Goddard-Kent-Olive Constructionp. 194
Gauged WZNW Modelsp. 197
NLSM and Stringsp. 203
Bosonic String NLSMp. 203
NLSM Approach to String LEEAp. 205
Zamolodchikov's c-Theoremp. 209
Conformally Invariant NLSM and Black Holesp. 211
Witten's Black Holep. 212
Exact String Black Hole Geometryp. 215
T-duality of Strings and NLSMp. 218
Non-Chiral Fermionic Strings in Curved Spacetimep. 221
N = 1 Neveu-Schwarz-Ramond NLSMp. 222
N = 2 Fermionic String NLSMp. 226
Anomalies of Bosonic and Fermionic Stringsp. 230
N = (2, 2) String Amplitudes and Integrabilityp. 237
Closed and Open (2, 2) Stringsp. 238
Mixed (2, 2) String Amplitudesp. 240
Chiral (1,0) NLSM and Heterotic Stringsp. 245
Anomalies of Heterotic NLSM in (1,0) Superspacep. 245
(1,0) Superspacep. 245
Background-Field Method in the Heterotic NLSMp. 249
Supergravitational and Superconformal Anomaliesp. 257
Chiral Coset Construction of Heterotic Stringsp. 270
Non-Abelian (1,0) Supersymmetric Chiral Bosonsp. 272
Non-Chiral (1, 0) Supersymmetric Coset Modelsp. 279
Chiral (1,0) Supersymmetric Coset Modelsp. 281
Anomalies of (1,0) Supersymmetric Coset Modelsp. 284
Anomaly-Free Solutionsp. 290
No Siegel Anomaly in the D = 4 Heterotic NLSMp. 292
LEEA in 4d, N = 2 Gauge Field Theoriesp. 295
Motivation and Setupp. 296
4d, N = 2 Gauge LEEA in the Coulomb Branchp. 300
On Instanton Calculationsp. 301
Seiberg-Witten Curvep. 302
Next-to-Leading Order Correction to the SW Actionp. 304
Hypermultiplet LEEA in 4dp. 307
Hypermultiplet LEEA in the Coulomb Branchp. 308
N = 2 Reduction from HSS to PSSp. 315
Exact Hypermultiplet LEEA in the Higgs Branchp. 316
Atiyah-Hitchin Metric and Elliptic Curvep. 319
Hypermultiplet LEEA in the Presence of FI Termp. 321
Brane Technologyp. 323
11d Supergravity and Its BPS Solutionsp. 324
NS and D Branes in Ten Dimensionsp. 327
Intersecting Branesp. 331
LEEA in the World-Volume of Type-IIA BPS Branesp. 332
M-Theory Resolutionp. 336
SW Solution and M5-Brane Dynamicsp. 338
On Supersymmetry Breaking and Confinementp. 342
Generalizations of NLSMp. 347
Dynamical Generation of Particles in 4d, N = 2 ALE NLSMp. 347
4d, N = 2 NLSM with ALE Metricp. 349
Quantized ALE N = 2 NLSM and Composite Particlesp. 352
Relation to M-Theory and Brane Technologyp. 358
D Brane Actions as NLSMp. 362
D-Brane Actions in Componentsp. 362
Born Ilfeld Actionp. 365
N = 1 Supersymmetric Born Infeld Actionp. 369
N = 2 Supersymmetric Born Infeld Actionp. 372
Fourth-Order NLSMp. 377
Bosonic 4d NLSM with Higher Derivativesp. 378
4d, N =1 NLSM with Higher Derivativesp. 384
4d, N = 2 NLSM with Higher Derivativesp. 392
Extended 4d Supergravities and U-Dualityp. 396
Referencesp. 399
Text Abbreviationsp. 415
Indexp. 417
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540674610
ISBN-10: 3540674616
Series: Theoretical and Mathematical Physics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 420
Published: 14th September 2000
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 24.23 x 16.54  x 3.0
Weight (kg): 0.77

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