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.

‘Harmonic Superspace … is the first discussion, outside of the confines of the research literature, to present pedagogically the intricacies of its topic. This is a unique book.’

Source: Physics Today

‘… it deserves a place in every theoretical physics and mathematics library. It is clearly all set to become the standard work on all things pertaining to Harmonic Superspace … this is a book that people will want to go back to.’

Source: Contemporary Physics