"Root" Action for N=4 Supersymmetric Mechanics Theories

TL;DR

The paper introduces a 'root' supermultiplet for N=4 supersymmetric mechanics, providing a reduction scheme to derive various supermultiplets and their actions, including superconformal and interaction terms, from a general sigma-model framework.

Contribution

It presents a novel reduction scheme from a 'root' supermultiplet to other N=4 supermultiplets, enabling systematic derivation of their actions and interactions.

Findings

Derived explicit reduction from the 'root' multiplet to other supermultiplets.

Constructed N=4 supersymmetric actions with potential and magnetic interactions.

Revealed that known superconformal actions emerge naturally from the reduction process.

Abstract

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 byproduct, 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.