N=8 Supersymmetric Quaternionic Mechanics

TL;DR

This paper constructs an N=8 supersymmetric mechanics model with specific degrees of freedom, extending from N=4 superspace, including potential terms, and explores the potential for N=9 supersymmetry.

Contribution

It develops an explicit N=8 supersymmetric mechanics model starting from N=4 harmonic superspace, adding Fayet-Iliopoulos terms, and analyzing its Hamiltonian structure.

Findings

Successfully constructed N=8 supersymmetric mechanics with potential terms.

Derived explicit Hamiltonian and Poisson brackets for the model.

Discussed the theoretical possibility of extending to N=9 supersymmetry.

Abstract

We construct N=8 supersymmetric mechanics with four bosonic end eight fermionic physical degrees of freedom. Starting from the most general N=4 superspace action in harmonic superspace for the ({\bf 4,8,4}) supermultiplet we find conditions which make it N=8 invariant. We introduce in the action Fayet-Iliopoulos terms which give rise to potential terms. We present the action in components and give explicit expressions for the Hamiltonian and Poisson brackets. Finally we discuss the possibility of N=9 supersymmetric mechanics.