Generalized Hyperkaehler Geometry and Supersymmetry

TL;DR

This paper introduces a new framework called (twisted) generalized hyperkaehler geometry, linking it to supersymmetric sigma models and constructing its twistor space to advance understanding in mathematical physics.

Contribution

It defines generalized hyperkaehler geometry and establishes its connection to supersymmetry, also constructing the associated twistor space for the first time.

Findings

Defined (twisted) generalized hyperkaehler geometry.

Linked the geometry to supersymmetric sigma models.

Constructed the twistor space for this geometry.

Abstract

We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.