Duality transformations and most general matter self-couplings in N = 2 supersymmetry

Abstract

The N = 2 matter off-shell representations with a finite set of field components are reformulated in the harmonic superspace approach. Their list includes all such multiplets known previously (the tensor multiplets, the relaxed hypermultiplet, the further relaxed hypermultiplet) as well as those newly introduced (higher relaxed ones, etc.). All these multiplets are described by constrained (and sometimes having a gauge freedom) analytic harmonic superfields. A manifestly N = 2 supersymmetric duality transformation is defined. By means of it all the self-couplings of the above superfields are shown to be dual equivalent to certain subclasses of general self-couplings of the basic analytic unconstrained N = 2 matter superfield having an infinite number of components, the q + hypermultiplet. This confirms our suggestion that the most general q + action yields the most general matter self-coupling in rigid N = 2 supersymmetry. The N = 2 matter actions are known to produce hyper-Kähler σ models in the physical boson sector. So, the relevant analytic superfield lagrangian density L (+4)( q +,...) can be regarded as the general “hyper-Kähler potential”, plausibly resulting in all possible hyper-Kähler metrics.