N=8 supersymmetric mechanics on the sphere S^3

TL;DR

This paper constructs a new nonlinear N=8 supersymmetric mechanics model on the sphere S^3 by reducing quaternionic supersymmetric mechanics, revealing a complex geometry described by Laplace's equation and potential terms.

Contribution

It introduces a novel nonlinear off-shell supermultiplet with three bosons and eight fermions derived from quaternionic N=8 mechanics, expanding the understanding of supersymmetric sigma-models on curved spaces.

Findings

The bosonic sector geometry is governed by an arbitrary function satisfying Laplace's equation on S^3.

Potential terms arise from a constant in the supermultiplet, which can be dualized to restore four bosonic degrees.

The resulting sigma-model exhibits high nonlinearity and complex geometric structure.

Abstract

Starting from quaternionic N=8 supersymmetric mechanics we perform a reduction over a bosonic radial variable, ending up with a nonlinear off-shell supermultiplet with three bosonic end eight fermionic physical degrees of freedom. The geometry of the bosonic sector of the most general sigma-model type action is described by an arbitrary function obeying the three dimensional Laplace equation on the sphere S^3. Among the bosonic components of this new supermultiplet there is a constant which gives rise to potential terms. After dualization of this constant one may come back to the supermultiplet with four physical bosons. However, this new supermultiplet is highly nonlinear. The geometry of the corresponding sigma-model action is briefly discussed.