Hyper-K�hler metrics and harmonic superspace

Abstract

The most general unconstrained superfield action for self-interactingN=2 matter hypermultiplets in analyticN=2 superspace is argued to produce a most generalN=2 hyper-Kähler σ-model after eliminating an infinite set of auxiliary fields. This suggests a new possibility of classifying hyper-Kähler metrics according to theN=2 analytic superfield self-interactions and provides an effective tool to compute these metrics explicitly. As the simplest example the U(2)-invariant quartic self-coupling of a singleq-hypermultiplet is analyzed and is shown to yield the familiar Taub-NUT metric. To see the geometric pattern directly in terms ofN=2 superfields we introduce a new on-shell representation ofq-hypermultiplets inN=2 harmonic superspace similar to the τ-description ofN=2 gauge theories. For the U(2)-example this formulation is checked to coincide with that by Sierra and Townsend.