Strong K\"ahler with Torsion as Generalised Geometry

TL;DR

This paper explores the representation of Strong Kähler with Torsion geometry within the framework of Generalised Complex Geometry, extending the analogy from supersymmetric sigma models to a broader geometric context.

Contribution

It introduces a novel way to describe Strong Kähler with Torsion using Generalised Complex Geometry, expanding the understanding of target space geometries in supersymmetric models.

Findings

Establishes a correspondence between Strong Kähler with Torsion and Generalised Complex Geometry.

Provides an analogy to the Gualtieri map for (2,1) and (2,0) supersymmetric models.

Enhances the geometric toolkit for analyzing supersymmetric sigma models.

Abstract

Strong K\"ahler with Torsion is the target space geometry of $(2,1)$ and $(2,0)$ supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of $(2,2)$ supersymmetric nonlinear sigma models to Generalised K\"ahler Geometry.