Galperin A.S., Ivanov E.A., Ogievetsky V.I., Sokatchev E.S. Harmonic Superspace

Cambridge University Press, 2007 — 324 pp. — (Cambridge Monographs on Mathematical Physics). — ISBN: 9780521020428.Here is the first pedagogical introduction to harmonic superspace in extended supersymmetry by the scientists who developed the method. Inspired by 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.Written by world experts in the field and the inventors of the harmonic superspace technique
Comprehensive and pedagogical in its approach
Complements other key texts on superstring theory in the same seriesIntroductory overview
Elements of supersymmetry
Superspace
Harmonic analysis
N=2 matter with infinite sets of auxiliary fields
N=2 matter multiplets with a finite number of auxiliary fields. N=2 duality transformations
Supersymmetric Yang-Mills theories
Harmonic supergraphs
Conformal invariance in N=2 harmonic superspace
Supergravity
Hyper-Kähler geometry in harmonic space
N=3 supersymmetric Yang-Mills theory
Conclusions