Current Algebra and Generalised Cartan Geometry

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.