ISBN: 3-540-67461-6
TITLE: Quantum Non-linear Sigma-Models
AUTHOR: Ketov, Sergei V.
TOC:

1. Introduction 1
2. Classical Structure and Renormalization 5
2.1 Bosonic NLSM: Definition and Examples 5
2.2 Covariant Background-Field Method 10
2.3 Regularization and Quantum Ambiguities 18
2.4 NLSM Renormalization Group beta-Functions 22
2.4.1 One-Loop Results 23
2.4.2 Two-Loop Results 24
2.4.3 Three-Loop Results 31
2.5 Buscher Duality and the Freedman-Townsend Model 42
2.6 Gauging NLSM Isometries 48
2.7 Skyrme NLSM of Pions and Nucleons 50
3. Supersymmetric NLSM 57
3.1 N = 1 NLSM Action and Background-Field Method 58
3.2 The Supersymmetric NLSM beta-Functions 63
3.2.1 One-Loop Results 63
3.2.2 Two-Loop Results 64
3.2.3 Three-Loop Results 66
3.2.4 Four-Loop Results 68
3.3 NLSM on Homogeneous Spaces 80
3.4 Gauging NLSM Isometries 83
3.4.1 N = 1 NLSM in 4d, and Khler Geometry 83
3.4.2 Gauging Isometries of 4d, N = 1 NLSM 87
4. NLSM and Extended Superspace 91
4.1 Complex Geometry and NLSM 93
4.1.1 ABC of Complex Geometry 94
4.1.2 4d, N = 2 NLSM in N = 1 Superspace 96
4.1.3 Triholomorphic Isometries of N = 2 NLSM 98
4.1.4 Gauging N = 2 NLSM Isometries in N = 1 Superspace 101
4.2 Special Geometry and Renormalization 103
4.2.1 N = 2 Susy and Restricted Chiral Superfields in 4d 103
4.2.2 Dimensional Reduction and 2d, N = 4 Special NLSM 109
4.2.3 UV-Finiteness Versus Non-Renormalizability 113
4.3 NLSM in Projective Superspace 118
4.3.1 N = 2 Tensor Multiplet and Its Generalizations in 4d 119
4.3.2 Reduction to 4d, N = 1 Superspace and Components 122
4.3.3 Quaternionic Geometry and Extended Supersymmetry 130
4.3.4 Perturbation Theory in Extended Superspace 138
4.4 Hyper-Khler Metrics and Harmonic Superspace 141
4.4.1 Four-Dimensional Hyper-Khler Metrics 142
4.4.2 Harmonic Superspace 150
4.4.3 Hyper-Khler NLSM in HSS 155
4.4.4 Gauging N = 2 NLSM Isometries in HSS 161
5. NLSM and 2d Conformal Field Theory 165
5.1 WZNW Models and Their Symmetries 165
5.1.1 2d Conformal Invariance 165
5.1.2 AKM Symmetries and SS Construction 172
5.1.3 WZNW Models and Topological Quantization 176
5.2 Super-WZNW Models and Their Symmetries 180
5.2.1 Superconformal and Super-AKM Algebras 181
5.2.2 N = 1 and N = 2 Supersymmetric WZNW Models 186
5.3 Coset Construction and Gauged WZNW Models 194
5.3.1 Goddard-Kent-Olive Construction 194
5.3.2 Gauged WZNW Models 197
6. NLSM and Strings 203
6.1 Bosonic String NLSM 203
6.1.1 NLSM Approach to String LEEA 205
6.1.2 Zamolodchikov's c-Theorem 209
6.2 Conformally Invariant NLSM and Black Holes 211
6.2.1 Witten's Black Hole 212
6.2.2 Exact String Black Hole Geometry 215
6.2.3 T-duality of Strings and NLSM 218
6.3 Non-Chiral Fermionic Strings in Curved Spacetime 221
6.3.1 N = 1 Neveu-Schwarz-Ramond NLSM 222
6.3.2 N = 2 Fermionic String NLSM 226
6.3.3 Anomalies of Bosonic and Fermionic Strings 230
6.4 N = (2, 2) String Amplitudes and Integrability 237
6.4.1 Closed and Open (2, 2) Strings 238
6.4.2 Mixed (2, 2) String Amplitudes 240
7. Chiral (1,0) NLSM and Heterotic Strings 245
7.1 Anomalies of Heterotic NLSM in (1, 0) Superspace 245
7.1.1 (1, 0) Superspace 245
7.1.2 Background-Field Method in the Heterotic NLSM 249
7.1.3 Supergravitational and Superconformal Anomalies 257
7.2 Chiral Coset Construction of Heterotic Strings 270
7.2.1 Non-Abelian (1, 0) Supersymmetric Chiral Bosons 272
7.2.2 Non-Chiral (1, 0) Supersymmetric Coset Models 279
7.2.3 Chiral (1, 0) Supersymmetric Coset Models 281
7.2.4 Anomalies of (1, 0) Supersymmetric Coset Models 284
7.2.5 Anomaly-Free Solutions 290
7.2.6 No Siegel Anomaly in the D = 4 Heterotic NLSM 292
8. LEEA in 4d, N = 2 Gauge Field Theories 295
8.1 Motivation and Setup 296
8.2 4d, N = 2 Gauge LEEA in the Coulomb Branch 300
8.2.1 On Instanton Calculations 301
8.2.2 Seiberg-Witten Curve 302
8.2.3 Next-to-Leading Order Correction to the SW Action 304
8.3 Hypermultiplet LEEA in 4d 307 
8.3.1 Hypermultiplet LEEA in the Coulomb Branch 308
8.3.2 N = 2 Reduction from HSS to PSS 315
8.3.3 Exact Hypermultiplet LEEA in the Higgs Branch 316
8.3.4 Atiyah-Hitchin Metric and Elliptic Curve 319
8.3.5 Hypermultiplet LEEA in the Presence of FI Term 321
8.4 Brane Technology 323
8.4.1 11d Supergravity and Its BPS Solutions 324
8.4.2 NS and D Branes in Ten Dimensions 327
8.4.3 Intersecting Branes 331
8.4.4 LEEA in the World-Volume of Type-IIA BPS Branes 332
8.4.5 M-Theory Resolution 336
8.4.6 SW Solution and M5-Brane Dynamics 338
8.5 On Supersymmetry Breaking and Confinement 342
9. Generalizations of NLSM 347
9.1 Dynamical Generation of Particles
in 4d, N = 2 ALE NLSM 347
9.1.1 4d, N = 2 NLSM with ALE Metric 349
9.1.2 Quantized ALE N = 2 NLSM and Composite Particles 352
9.1.3 Relation to M-Theory and Brane Technology 358
9.2 D-Brane Actions as NLSM 362
9.2.1 D-Brane Actions in Components 362
9.2.2 Born-Infeld Action 365
9.2.3 N = 1 Supersymmetric Born-Infeld Action 369
9.2.4 N = 2 Supersymmetric Born-Infeld Action 372
9.3 Fourth-Order NLSM 377
9.3.1 Bosonic 4d NLSM with Higher Derivatives 378
9.3.2 4d, N = 1 NLSM with Higher Derivatives 384
9.3.3 4d, N = 2 NLSM with Higher Derivatives 392
9.4 Extended 4d Supergravities and U-Duality 396
References 399
Text Abbreviations 415
Index 417
END
