Root Action for N=4 Supersymmetric Mechanics Theories

We propose to consider the N=4,d=1 supermultiplet with (4,4,0) component content as a “root” one. We elaborate a new reduction scheme from the root multiplet to supermultiplets with a smaller number of physical bosons. Starting from the most general sigma-model-type action for the root multiplet, we explicitly demonstrate that the actions for the rest of linear and nonlinear N=4 supermultiplets can be easily obtained by reduction. Within the proposed reduction scheme, there is a natural possibility to introduce Fayet-Iliopoulos terms. In the reduced systems, such terms give rise to potential terms, and in some cases also to terms describing the interaction with a magnetic field. We demonstrate that known N=4 superconformal actions, together with their possible interactions, appear as results of the reduction from a free action for the root supermultiplet. As a by-product, we also construct an N=4 supersymmetric action for the linear (3,4,1) supermultiplet, containing both an interaction with a Dirac monopole and a harmonic oscillator-type potential, generalized for arbitrary conformally flat metrics.