Complex Geometry and Supersymmetry

TL;DR

This paper explores how sigma models with (2, 2) supersymmetry are characterized by different aspects of Generalized Kähler Geometry depending on the number of manifest supersymmetries, highlighting geometric variations.

Contribution

It clarifies the relationship between supersymmetry manifestness and the geometric structures in sigma models, emphasizing the role of Generalized Kähler Geometry.

Findings

Different formulations of sigma models correspond to different aspects of Generalized Kähler Geometry.

The number of manifest supersymmetries influences the geometric description of the models.

The geometric structures underlying supersymmetric sigma models are classified by their supersymmetry properties.

Abstract

I stress how the form of sigma models with (2, 2) supersymmetry differs depending on the number of manifest supersymmetries. The differences correspond to different aspects/formulations of Generalized K\"ahler Geometry.