K\"ahler geometry and SUSY mechanics

TL;DR

This paper explores two supersymmetric mechanics models linked to K"ahler geometry, highlighting their structures and relations to antisymplectic geometry, with one model being a known N=4 sigma-model and the other an N=2 SUSY system.

Contribution

It introduces a new N=2 SUSY mechanics model on K"ahler manifolds and discusses its connection to antisymplectic geometry, expanding the understanding of SUSY models in geometric contexts.

Findings

The N=4 supersymmetric sigma-model is revisited and analyzed.

A novel N=2 SUSY mechanics model on K"ahler manifolds is proposed.

Relations between SUSY mechanics and antisymplectic geometry are discussed.

Abstract

We present two examples of SUSY mechanics related with K\"ahler geometry. The first system is the N=4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N=2 SUSY mechanics whose phase space is the external algebra of an arbitrary K\"ahler manifold. The relation of these models with antisymplectic geometry is discussed.