| Introduction | p. 1 |
| Classical Structure and Renormalization | p. 5 |
| Bosonic NLSM: Definition and Examples | p. 5 |
| Covariant Background-Field Method | p. 10 |
| Regularization and Quantum Ambiguities | p. 18 |
| NLSM Renormalization Group ß-Functions | p. 22 |
| One-Loop Results | p. 23 |
| Two-Loop Results | p. 24 |
| Three-Loop Results | p. 31 |
| Buscher Duality and the Freedman-Townsend Model | p. 42 |
| Gauging NLSM Isometries | p. 48 |
| Skyrme NLSM of Pions and Nucleons | p. 50 |
| Supersymmetric NLSM | p. 57 |
| N = 1 NLSM Action and Background-Field Method | p. 58 |
| The Supersymmetric NLSM ß-Functions | p. 63 |
| One-Loop Results | p. 63 |
| Two-Loop Results | p. 64 |
| Three-Loop Results | p. 66 |
| Four-Loop Results | p. 68 |
| NLSM on Homogeneous Spaces | p. 80 |
| Gauging NLSM Isometries | p. 83 |
| N =1 NLSM in 4d, and Kähler Geometry | p. 83 |
| Gauging Isometries of 4d, N = 1 NLSM | p. 87 |
| NLSM and Extended Superspace | p. 91 |
| Complex Geometry and NLSM | p. 93 |
| ABC of Complex Geometry | p. 94 |
| 4d, N = 2 NLSM in N = 1 Superspace | p. 96 |
| Triholomorphic Isometries of N = 2 NLSM | p. 98 |
| Gauging N = 2 NLSM Isometries in N = 1 Superspace | p. 101 |
| Special Geometry and Renormalization | p. 103 |
| N = 2 Susy and Restricted Chiral Superfields in 4d | p. 103 |
| Dimensional Reduction and 2d, N = 4 Special NLSM | p. 109 |
| UV-Finiteness Versus Non-Renormalizability | p. 113 |
| NLSM in Projective Superspace | p. 118 |
| N = 2 Tensor Multiplet and Its Generalizations in 4d | p. 119 |
| Reduction to 4d, N =1 Superspace and Components | p. 122 |
| Quaternionic Geometry and Extended Supersymmetry | p. 130 |
| Perturbation Theory in Extended Superspace | p. 138 |
| Hyper-Kähler Metrics and Harmonic Superspace | p. 141 |
| Four-Dimensional Hyper-Kähler Metrics | p. 142 |
| Harmonic Superspace | p. 150 |
| Hyper-Kähler NLSM in HSS | p. 155 |
| Gauging N = 2 NLSM Isometries in HSS | p. 161 |
| NLSM and 2d Conformal Field Theory | p. 165 |
| WZNW Models and Their Symmetries | p. 165 |
| 2d Conformal Invariance | p. 165 |
| AKM Symmetries and SS Construction | p. 172 |
| WZNW Models and Topological Quantization | p. 176 |
| Super-WZNW Models and Their Symmetries | p. 180 |
| Superconformal and Super-AKM Algebras | p. 181 |
| N = 1 and N = 2 Supersymmetric WZNW Models | p. 186 |
| Coset Construction and Gauged WZNW Models | p. 194 |
| Goddard-Kent-Olive Construction | p. 194 |
| Gauged WZNW Models | p. 197 |
| NLSM and Strings | p. 203 |
| Bosonic String NLSM | p. 203 |
| NLSM Approach to String LEEA | p. 205 |
| Zamolodchikov's c-Theorem | p. 209 |
| Conformally Invariant NLSM and Black Holes | p. 211 |
| Witten's Black Hole | p. 212 |
| Exact String Black Hole Geometry | p. 215 |
| T-duality of Strings and NLSM | p. 218 |
| Non-Chiral Fermionic Strings in Curved Spacetime | p. 221 |
| N = 1 Neveu-Schwarz-Ramond NLSM | p. 222 |
| N = 2 Fermionic String NLSM | p. 226 |
| Anomalies of Bosonic and Fermionic Strings | p. 230 |
| N = (2, 2) String Amplitudes and Integrability | p. 237 |
| Closed and Open (2, 2) Strings | p. 238 |
| Mixed (2, 2) String Amplitudes | p. 240 |
| Chiral (1,0) NLSM and Heterotic Strings | p. 245 |
| Anomalies of Heterotic NLSM in (1,0) Superspace | p. 245 |
| (1,0) Superspace | p. 245 |
| Background-Field Method in the Heterotic NLSM | p. 249 |
| Supergravitational and Superconformal Anomalies | p. 257 |
| Chiral Coset Construction of Heterotic Strings | p. 270 |
| Non-Abelian (1,0) Supersymmetric Chiral Bosons | p. 272 |
| Non-Chiral (1, 0) Supersymmetric Coset Models | p. 279 |
| Chiral (1,0) Supersymmetric Coset Models | p. 281 |
| Anomalies of (1,0) Supersymmetric Coset Models | p. 284 |
| Anomaly-Free Solutions | p. 290 |
| No Siegel Anomaly in the D = 4 Heterotic NLSM | p. 292 |
| LEEA in 4d, N = 2 Gauge Field Theories | p. 295 |
| Motivation and Setup | p. 296 |
| 4d, N = 2 Gauge LEEA in the Coulomb Branch | p. 300 |
| On Instanton Calculations | p. 301 |
| Seiberg-Witten Curve | p. 302 |
| Next-to-Leading Order Correction to the SW Action | p. 304 |
| Hypermultiplet LEEA in 4d | p. 307 |
| Hypermultiplet LEEA in the Coulomb Branch | p. 308 |
| N = 2 Reduction from HSS to PSS | p. 315 |
| Exact Hypermultiplet LEEA in the Higgs Branch | p. 316 |
| Atiyah-Hitchin Metric and Elliptic Curve | p. 319 |
| Hypermultiplet LEEA in the Presence of FI Term | p. 321 |
| Brane Technology | p. 323 |
| 11d Supergravity and Its BPS Solutions | p. 324 |
| NS and D Branes in Ten Dimensions | p. 327 |
| Intersecting Branes | p. 331 |
| LEEA in the World-Volume of Type-IIA BPS Branes | p. 332 |
| M-Theory Resolution | p. 336 |
| SW Solution and M5-Brane Dynamics | p. 338 |
| On Supersymmetry Breaking and Confinement | p. 342 |
| Generalizations of NLSM | p. 347 |
| Dynamical Generation of Particles in 4d, N = 2 ALE NLSM | p. 347 |
| 4d, N = 2 NLSM with ALE Metric | p. 349 |
| Quantized ALE N = 2 NLSM and Composite Particles | p. 352 |
| Relation to M-Theory and Brane Technology | p. 358 |
| D Brane Actions as NLSM | p. 362 |
| D-Brane Actions in Components | p. 362 |
| Born Ilfeld Action | p. 365 |
| N = 1 Supersymmetric Born Infeld Action | p. 369 |
| N = 2 Supersymmetric Born Infeld Action | p. 372 |
| Fourth-Order NLSM | p. 377 |
| Bosonic 4d NLSM with Higher Derivatives | p. 378 |
| 4d, N =1 NLSM with Higher Derivatives | p. 384 |
| 4d, N = 2 NLSM with Higher Derivatives | p. 392 |
| Extended 4d Supergravities and U-Duality | p. 396 |
| References | p. 399 |
| Text Abbreviations | p. 415 |
| Index | p. 417 |
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