Hyper-Kaehler geometry and dualization

TL;DR

This paper shows how to dualize auxiliary fields into physical ones in N=8 supersymmetric mechanics, resulting in a hyper-Kaehler bosonic manifold, by employing different dualization methods for each auxiliary field.

Contribution

It introduces a novel dualization approach in N=8 supersymmetric mechanics that yields hyper-Kaehler geometries through distinct auxiliary field transformations.

Findings

Dualization of auxiliary fields produces hyper-Kaehler manifolds.

Different dualization methods are applied to auxiliary fields.

The approach clarifies the analogy with three-dimensional cases.

Abstract

We demonstrate that in N=8 supersymmetric mechanics with linear and nonlinear chiral supermultiplets one may dualize two auxiliary fields into physical ones in such a way that the bosonic manifold will be a hyper-Kaehler one. The key point of our construction is about different dualizations of the two auxiliary components. One of them is turned into a physical one in the standard way through its replacement by the total time derivative of some physical field. The other auxiliary field is dualized through a Lagrange multiplier. We clarify this choice of dualization by presenting the analogy with a three-dimensional case.