A note on N=4 supersymmetric mechanics on K\"ahler manifolds

TL;DR

This paper introduces geometric models of N=4 supersymmetric mechanics on Kähler manifolds, connecting them to two-dimensional sigma-models and exploring their relation to antisymplectic geometry.

Contribution

It proposes new geometric models of N=4 supersymmetric mechanics on Kähler supermanifolds, extending the understanding of supersymmetric phase spaces.

Findings

Models are related to 2D N=2 supersymmetric sigma-models.

Phase space can be a Kähler supermanifold.

Connections to antisymplectic geometry are discussed.

Abstract

The geometric models of N=4 supersymmetric mechanics with $(2d.2d)_{\DC}$-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models by Alvarez-Gaum\'e and Freedman. The related construction of supersymmetric mechanics whose phase space is a K\"ahler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.