Dual superfield approach to supersymmetric mechanics with spin variables

Abstract

We consider a reducible $\mathcal{N}=4$, $d=1$ multiplet described by a real superfield as a coupling of the mirror $(1,4,3)$ and ordinary $(3,4,1)$ 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 $\mathcal{N}=4$ long multiplet can be derived from an irreducible SU(2$|$2) multiplet.

1+11 pages; v3: changes in Sections 1 and 4, reference added