Eguchi-Hanson type metrics from harmonic superspace

Harmonic superspace provides a framework for constructing general hyper-Kahler metrics. The simple example of the Taub-NUT manifold was given previously. Here it is shown that the harmonic superspace Lagrangian Lsup((+4)) = 1/4 [(D++ω)2-(xi++)2ω-2] for a single interacting hypermultiplet describes an N=2 supersymmetric hyper-Kahler σ model with the d=4 Eguchi-Hanson instanton as its target manifold. The potential ω-2 is the unique one invariant with respect to a Pauli-Gursey-like SU(2) group. Other harmonic superspace actions are presented which it is expected, will yield some other interesting metrics, including the multi-Eguchi-Hanson and Calabi ones, etc. (author)