Super W-Symmetries, Covariantly Constant Forms And Duality Transformations

TL;DR

This paper explores how covariantly constant forms in supersymmetric sigma models relate to conserved currents and super W-algebras, and how duality transformations generate new forms that further restrict the manifold's holonomy group.

Contribution

It demonstrates that duality transformations produce new covariantly constant forms, extending the understanding of holonomy restrictions in supersymmetric sigma models.

Findings

Duality transformations generate new covariantly constant forms.

Covariantly constant forms are linked to super W-algebras and conserved currents.

Holonomy groups are restricted by the existence of these forms.

Abstract

On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the holonomy group of the manifold. Via duality transformation we get new covariantly constant forms, thus restricting the holonomy group of the new manifold.