Dual multiplets in N=4 superconformal mechanics

TL;DR

This paper develops Lagrangian models for three-particle N=4 superconformal mechanics using standard and twisted supermultiplets, revealing a symmetry in the potential structure and constructing known and new models with explicit examples.

Contribution

It introduces a novel formulation of three-particle N=4 superconformal mechanics using twisted supermultiplets and explores the symmetry of the potential under a specific transformation.

Findings

Models produce similar systems with flipped angular potentials.

Explicit construction of 3-Calogero, BC2, and G2 models.

New examples of 3D 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.