Towards an invariant geometry of double field theory

TL;DR

This paper develops an invariant geometric framework for double field theory, unifying previous formulations and analyzing the properties of generalized curvature tensors without relying on specific bases.

Contribution

It introduces a basis-independent geometric approach to double field theory, connecting it with generalized geometry and analyzing the information contained in the generalized Riemann tensor.

Findings

Generalized Riemann tensor includes Ricci and scalar curvature

The framework unifies frame-like and metric-like formulations

The generalized Riemann tensor does not encode the full Riemann tensor

Abstract

We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for the frame-like and metric-like formulations developed before. We discuss the relation to generalized geometry and give an `index-free' proof of the algebraic Bianchi identity. Finally, we analyze to what extent the generalized Riemann tensor encodes the curvatures of Riemannian geometry. We show that it contains the conventional Ricci tensor and scalar curvature but not the full Riemann tensor, suggesting the possibility of a further extension of this framework.