Gauged Double Field Theory, Current Algebras and Heterotic Sigma Models

We study the $O(D,D+n)$ generalized metric and the gauge symmetries in the gauged double field theory (DFT) in view of current algebras and sigma models. We show that the $O(D,D+n)$ generalized metric in the gauged DFT is consistent with the heterotic sigma models at the leading order in the ${\alpha }^{\mathrm{\prime }}$-corrections. We then study the non-Abelian gauge symmetries and current algebras of heterotic string theories. We show that the algebras exhibit the correct diffeomorphism, the $B$-field gauge transformations of the background fields together with the non-Abelian gauge transformations possibly with the appropriate local Lorentz transformations.