Deformed Weitzenböck Connections and Double Field Theory

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.