Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models

TL;DR

This paper explores the connection between generalized complex geometry and N=(2,2) supersymmetric nonlinear sigma-models, revealing how generalized Kahler structures naturally emerge in this context.

Contribution

It demonstrates a formulation of N=(2,2) sigma-models using semi-(anti)chiral multiplets that naturally incorporate auxiliary fields and elucidates the geometric structures involved.

Findings

Generalized complex structures commute in this framework.

The metric, B-field, and structures are derived from a single potential K.

The formulation clarifies the geometric interpretation of supersymmetric sigma-models.

Abstract

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N=(2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.