Global Symmetries of Quaternion-K$\bf \ddot{a}$hler ${\cal N}=4$ Supersymmetric Mechanics

TL;DR

This paper investigates the global symmetries of ${ m N}=4$ supersymmetric mechanics with Quaternion-K"ahler target spaces, revealing that all associated Noether charges vanish on-shell, indicating a highly constrained Hamiltonian structure.

Contribution

It provides a detailed Hamiltonian analysis of ${ m N}=4$ supersymmetric mechanics on Quaternion-K"ahler spaces, highlighting the vanishing of all Noether charges due to equations of motion.

Findings

All Noether charges vanish on-shell.

The system is highly constrained by equations of motion.

Complete Hamiltonian analysis of the bosonic sector is performed.

Abstract

We analyze the global symmetries of ${\cal N}=4$ supersymmetric mechanics involving $4n$-dimensional Quaternion-K\"ahler (QK) $1D$ sigma models on projective spaces $\mathbb{H}{\rm H}^n$ and $\mathbb{H}{\rm P}^n$ as the bosonic core. All Noether charges associated with global worldline symmetries are shown to vanish as a result of equations of motion, which implies that we deal with a severely constrained hamiltonian system. The complete hamiltonian analysis of the bosonic sector is performed.