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Klappentext This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory! it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories! both at the classical and quantum levels. Furthermore! they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry! namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories! for example! the one-to-one correspondence between N=2 supersymmetric matter! and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory! string theory and complex geometries. Zusammenfassung Inspired by exciting developments in superstring theory! this is a pedagogical and comprehensive introduction to the harmonic superspace method in extended supersymmetry. The authors (credited with inventing the technique) are recognised as world experts on the subject and present a clear account of its formalism and applications. Inhaltsverzeichnis Preface; 1. Introductory overview; 2. Elements of supersymmetry; 3. Superspace; 4. Harmonic analysis; 5. N=2 matter with infinite sets of auxiliary fields; 6. N=2 matter multiplets with a finite number of auxiliary fields. N=2 duality transformations; 7. Supersymmetric Yang-Mills theories; 8. Harmonic supergraphs; 9. Conformal invariance in N=2 harmonic superspace; 10. Supergravity; 11. Hyper-Kähler geometry in harmonic space; 12. N=3 supersymmetric Yang-Mills theory; 13. Conclusions; Appendix. Notations, conventions and useful formulas; References; Index.
