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

摘要

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 Noethercurrent and corresponding Noether potential associated with unified gaugeinvariance. We add Wald-type counter two-form to the Noether potential anddefine conserved global charges as surface integral. We check our$\mathbf{O}(D,D)$ covariant formula against various string backgrounds, bothgeometric and non-geometric. In all cases we examined, we find perfectagreements with previous results. Our formula facilitates to evaluate momentaalong not only ordinary spacetime directions but also dual spacetime directionson equal footing. From this, we confirm recent assertion that null wave indoubled spacetime is the same as macroscopic fundamental string in ordinaryspacetime.