We propose to consider the $\mathcal{N}=4,d=1$ supermultiplet with $(\mathbf{4},\mathbf{4},\mathbf{0})$ 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 $\mathcal{N}=4$ 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 $\mathcal{N}=4$ 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 $\mathcal{N}=4$ supersymmetric action for the linear $(\mathbf{3},\mathbf{4},\mathbf{1})$ supermultiplet, containing both an interaction with a Dirac monopole and a harmonic oscillator-type potential, generalized for arbitrary conformally flat metrics.

• Received 24 November 2005

DOI:https://doi.org/10.1103/PhysRevD.73.025011