$\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory

TL;DR

This paper develops an $ extbf{O}(D,D)$ covariant framework for deriving conserved Noether currents and charges in double field theory, enabling unified treatment of geometric and non-geometric backgrounds and dual spacetime directions.

Contribution

It introduces a covariant formula for Noether currents and global charges in double field theory, validated against various string backgrounds, including non-geometric cases.

Findings

Perfect agreement with previous results in tested backgrounds

Allows evaluation of momenta in dual spacetime directions

Confirms null wave in doubled spacetime as fundamental string

Abstract

Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariance. We add Wald-type counter two-form to the Noether potential and define conserved global charges as surface integral. We check our $\mathbf{O}(D,D)$ covariant formula against various string backgrounds, both geometric and non-geometric. In all cases we examined, we find perfect agreements with previous results. Our formula facilitates to evaluate momenta along not only ordinary spacetime directions but also dual spacetime directions on equal footing. From this, we confirm recent assertion that null wave in doubled spacetime is the same as macroscopic fundamental string in ordinary spacetime.