Note on $\mathcal{N}=8$ supersymmetric mechanics with dynamical and semi-dynamical multiplets

TL;DR

This paper presents a Hamiltonian formulation of a recently proposed $ =8$ supersymmetric mechanics model, revealing its superconformal symmetry and geometric structure, with implications for understanding supersymmetric systems with cone-like target spaces.

Contribution

It provides the first Hamiltonian formulation of the $ =8$ supersymmetric mechanics model with dynamical and semi-dynamical multiplets, demonstrating its superconformal symmetry and geometric interpretation.

Findings

The model exhibits $ ext{osp}(8|2)$ superconformal symmetry.

The bosonic part describes a free particle on an eight-dimensional cone.

The fermionic part acts as a spin-orbit interaction term.

Abstract

We give a Hamiltonian formulation of the new model of $\mathcal{N}=8$ supersymmetric mechanics recently proposed by S.~Fedoruk and E.~Ivanov and show that it possesses the dynamical $\mathcal{N}=8$ superconformal symmetry $osp(8|2)$. The bosonic part of the Hamiltonian is just a free particle on eight-dimensional cone embedded in nine-dimensional pseudo-Euclidean space, while the fermionic part can be interpreted as a spin-orbit interaction term.