Generalized metric formulation of double field theory

TL;DR

The paper develops a manifestly $O(D,D)$-covariant formulation of double field theory using a generalized metric ${\cal H}_{MN}$ on a doubled spacetime, recasting gauge transformations as a linear generalized Lie derivative and showing closure via the C bracket. It presents an $O(D,D)$-invariant action and a generalized scalar curvature ${\cal R}$, proving gauge invariance and deriving a generalized Ricci tensor ${\cal R}_{MN}$ that encodes the dynamics of the metric and $B$-field in a unified framework. The results connect to generalized geometry and Siegel’s frame approach, illustrating how ${\cal H}$ can be viewed either as a composite of $g$ and $b$ or as a constrained fundamental field, and clarifying the role of D- and C-brackets in the gauge structure. The work sets the stage for a deeper geometric understanding of double field theory and highlights directions for extending to a fully doubled theory with a weaker constraint and broader geometric interpretation.

Abstract

The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.