Generalized dualities for heterotic and type I strings

We define generalized dualities for heterotic and type I strings based on consistent truncations to half-maximal gauged supergravities in more than three dimensions. The latter are constructed from a generalized Scherk-Schwarz ansatz in heterotic double field theory that satisfies the strong constraint. Necessary and sufficient conditions on the resulting embedding tensor are discussed, showing that only certain gaugings, called geometric, can arise from this procedure. For all of them, we explicitly construct the internal geometry and gauge potentials. In general, this construction is not unique and permits different uplifts which are used to define generalized T-duality. Two examples are worked out underlying the utility of our approach to explore new dualities and uplifts of half-maximal gauged supergravities.