Potentials in N=4 superconformal mechanics

TL;DR

This paper explores how adding potentials to N=4 superconformal mechanics preserves superconformal symmetry by modifying transformation properties, introducing auxiliary fermions, and resulting in spin-like interactions.

Contribution

It demonstrates that potentials can be incorporated into N=4 superconformal mechanics without breaking symmetry, through modified transformations and auxiliary fermionic couplings.

Findings

Adding harmonic oscillator potential preserves superconformal symmetry.

New auxiliary fermions act as spin degrees of freedom.

Constructed models are invariant under the full D(2,1;α) superconformal group.

Abstract

Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the transformation properties of the (super)fields. We also analyze the possibility to introduce potentials in N=4 supersymmetric mechanics by coupling it with auxiliary fermionic superfields. The new coupling we considered does not introduce new fermionic degrees of freedom - all our additional fermions are purely auxiliary ones. The new bosonic components have a first order kinetic term and therefore they serve as spin degrees of freedom. The resulting system contains, besides the potential term in the bosonic sector, a non-trivial spin-like interaction in the fermionic sector. The superconformal mechanics we constructed in this paper is invariant under the full $D(2,1;\alpha)$ superconformal group. This invariance is not evident and is achieved within modified (super)conformal transformations of the superfields.