Dual multiplets in N=4 superconformal mechanics

Abstract

We propose Lagrangian formulations of a three-particles translation invariant $N=4$ superconformal mechanics based on the standard and twisted $(1,4,3)$ supermultiplets. We show that in the appropriate set of coordinates, in which the bosonic kinetic terms for each of the two cases take conformally-flat forms, the corresponding models produce just similar physical systems with the flipped angular part of bosonic potential $U(x)\rightarrow 1/U(x)$. This flipping looks so simple only being written in the "angle" variable, while in the standard variables it looks more complicated to preserve the superconformal symmetry. We demonstrate at both the superfield and the component level, how familiar $N=4$ supersymmetric 3-particles models, including $3-Calogero$, ${\it BC_2}$ and ${\it G_2}$ ones, can be constructed with twisted supermultiplets. We also present some new explicit examples of 3-dimensional superconformal mechanics.