Generalized Kahler Geometry from supersymmetric sigma models

TL;DR

This paper provides a physical derivation of generalized Kahler geometry from supersymmetric sigma models, clarifying its relation to bi-hermitean geometry and discussing topological twists.

Contribution

It offers a new physical perspective on generalized Kahler geometry, connecting it with supersymmetric sigma models and rederiving key geometric equivalences.

Findings

Derived generalized Kahler geometry from supersymmetric sigma models.

Clarified the relation between Lagrangian and Hamiltonian formalisms.

Discussed topological twist in the context of generalized Kahler geometry.

Abstract

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.