Current Algebra and Generalised Cartan Geometry

TL;DR

This paper connects generalised curvature and torsion in O(d,d)-generalised geometry to Cartan geometry, providing a covariant framework for sigma model dynamics that unifies various geometric tensors.

Contribution

It demonstrates that the approach to generalised curvature and torsion extends Cartan geometry within the context of O(d,d)-generalised geometry, and applies this to covariant sigma model formulations.

Findings

Higher generalised tensors relate to covariant derivatives of the generalised Riemann tensor.

Framework unifies geometric tensors in a covariant formalism.

Enables covariant description of sigma model dynamics.

Abstract

This article shows that the approach to generalised curvature and torsion pioneered by Polacek and Siegel [1] is a generalisation of Cartan Geometry -- rendering latter natural from the point of view of O(d,d)-generalised geometry. We present this approach in the generalised metric formalism and show that almost all parts of the additional higher generalised tensors appearing in this approach correspond to covariant derivatives of the generalised Riemann tensor. As an application, we use this framework to phrase sigma model dynamics in an explicitly covariant way -- both under generalised diffeomorphisms and local gauge transformations.