Deformed Weitzenb\"ock Connections and Double Field Theory

TL;DR

This paper explores alternative geometric connections in Double Field Theory, expressing equations of motion through torsion and non-metricity, and introduces a Teleparallel equivalent of DFT.

Contribution

It introduces a generalized connection framework in DFT, including a Teleparallel formulation, expanding the geometric tools used in the theory.

Findings

Reformulation of DFT equations using torsion and non-metricity tensors

Definition of a generalized contorsion tensor in DFT

Establishment of a Teleparallel equivalent of DFT

Abstract

We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity tensors) based on other connections rather than the usual generalized Levi-Civita connection and the generalized Riemann curvature. We define a generalized contorsion tensor and obtain, as a particular case, the Teleparallel equivalent of Double Field Theory. To do this, we first need to revisit generic connections in standard geometry written in terms of first-order derivatives of the vielbein in order to obtain equivalent theories to Einstein Gravity (like for instance the Teleparallel Gravity case). The results are then easily extrapolated to DFT. This work supersedes arXiv:1706.09008