  We argue that off-shell dualities between d=1 supermultiplets with different
sets of physical bosonic components and the same number of fermionic ones are
related to gauging some symmetries in the actions of the supermultiplets with
maximal sets of physical bosons. Our gauging procedure uses off-shell
superfields and so is manifestly supersymmetric. We focus on N=4 supersymmetric
mechanics and show that various actions of the multiplet (3,4,1) amount to some
gauge choices in the gauged superfield actions of the linear or nonlinear
(4,4,0) multiplets. In particular, the conformally invariant (3,4,1)
superpotential is generated by the Fayet-Iliopoulos term of the gauge
superfield. We find a new nonlinear variant of the multiplet (4,4,0), such that
its simplest superfield action produces the most general 4-dim hyper-K\"ahler
metric with one triholomorphic isometry as the bosonic target metric. We also
elaborate on some other instructive examples of N=4 superfield gaugings,
including a non-abelian gauging which relates the free linear (4,4,0) multiplet
to a self-interacting (1,4,3) multiplet.

High Energy Physics - Theory