Frame-like Geometry of Double Field Theory

TL;DR

This paper connects two formulations of double field theory with a frame-like geometric formalism, providing a self-contained presentation and showing the equivalence of the resulting action to the original theory.

Contribution

It introduces a frame-like geometric formalism for double field theory, clarifying constraints and deriving curvature quantities, establishing equivalence with existing formulations.

Findings

Derived Riemann, Ricci tensors, and curvature scalar within the formalism

Demonstrated the curvature scalar defines an action equivalent to double field theory

Provided a self-contained presentation of the geometric formalism

Abstract

We relate two formulations of the recently constructed double field theory to a frame-like geometrical formalism developed by Siegel. A self-contained presentation of this formalism is given, including a discussion of the constraints and its solutions, and of the resulting Riemann tensor, Ricci tensor and curvature scalar. This curvature scalar can be used to define an action, and it is shown that this action is equivalent to that of double field theory.