Dual superfield approach to supersymmetric mechanics with spin variables

TL;DR

This paper introduces a new ${ m N}=4$, $d=1$ supermultiplet called the 'long multiplet' that combines mirror and ordinary multiplets, revealing hidden SU(2|2) supersymmetry and reproducing known models.

Contribution

It constructs a coupled system of dynamical and semi-dynamical multiplets using the long multiplet, extending supersymmetry to SU(2|2) and connecting to previous models.

Findings

Reproduces the 2012 Fedoruk-Ivanov-Lechtenfeld model

Reveals hidden SU(2|2) supersymmetry

Derives the ${ m N}=4$ long multiplet from an SU(2|2) multiplet

Abstract

We consider a reducible ${\cal N}=4$, $d=1$ multiplet described by a real superfield as a coupling of the mirror ${\bf (1, 4, 3)}$ and ordinary ${\bf (3, 4, 1)}$ multiplets. Employing this so-called "long multiplet", we construct a coupled system of dynamical and semi-dynamical multiplets. We show that the corresponding {\it on-shell} model reproduces the model of Fedoruk, Ivanov and Lechtenfeld presented in 2012. Furthermore, there is a hidden supersymmetry acting on the long multiplet that extends the full world-line supersymmetry to SU(2$|$2). In other words, the ${\cal N}=4$ long multiplet can be derived from an irreducible SU(2$|$2) multiplet.