Harmonic Superspace

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-Khler and quaternionic manifolds.