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A number of issues in heterotic double field theory are studied. Thisincludes the analysis of the T-dual configurations of a flat constant gaugeflux background, which turn out to be non-geometric. Performing a fieldredefinition to a non-geometric frame, these T-duals take a very simple formreminiscent of the constant Q- and R-flux backgrounds. In addition, it is shownhow the analysis of arXiv:1304.2784 generalizes to heterotic generalizedgeometry. For every field redefinition specified by an O(D,D+n) transformation,the structure of the resulting supergravity action is governed by thedifferential geometry of a corresponding Lie algebroid.

T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory