The O_{D,D} Geometry of String Theory

TL;DR

This paper develops a new geometric framework for double field theory using a special flat, torsionful connection compatible with the O_{D,D} structure, leading to an action consistent with gauged supergravity.

Contribution

It introduces a novel metric connection for double field theory that is compatible with the generalized metric and O_{D,D} structure, enabling a covariant formulation.

Findings

Constructed a torsionful, flat connection compatible with the generalized metric.

Derived a covariant derivative for double field theory.

Reproduced the doubled action consistent with gauged supergravity.

Abstract

We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the O_{D,D} structure. The connection is simultaneously torsionful and flat. Using this connection one may construct a proper covariant derivative for double field theory. We then write the doubled action in terms of the generalised torsion of this connection. This action then exactly reproduces that required for doubled field theory and gauged supergravity.