Holonomy groups and W-symmetries

TL;DR

This paper explores the relationship between holonomy groups, covariantly constant forms, and W-symmetries in irreducible sigma models on Riemannian spaces, revealing algebraic structures and supersymmetry extensions.

Contribution

It establishes a connection between special geometric structures and W-algebras in supersymmetric sigma models, highlighting the role of holonomy and covariantly constant forms.

Findings

Holonomy groups characterize special geometries in sigma models.

Covariantly constant forms lead to symmetries described by W-algebras.

Extended supersymmetries are specific cases within this framework.

Abstract

Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant forms which in turn give rise to symmetries of the supersymmetric sigma model actions. The Poisson bracket algebra of the corresponding currents is a W-algebra. Extended supersymmetries arise as special cases.