Double field theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of α ′ is invariant under global O ( D , D ) transformations and ought to be invariant under gauge transformations which receive α ′ -corrections. On the other hand, the effective theory in the usual D -dimensional formulation of string theory is manifestly gauge invariant and ought to be invariant under T-duality transformations which receive α ′ -corrections. We speculate that the combination of these two constraints may fix both the 2 D -dimensional and the D -dimensional effective actions without knowledge of the α ′ -corrections of the gauge and the T-duality transformations. In this paper, using generalized fluxes, we construct arbitrary O ( D , D ) -invariant actions at orders α ′ 0 and α ′ , and then dimensionally reduce them to the D -dimensional spacetime. On the other hand, at these orders, we construct arbitrary covariant D -dimensional actions. Constraining the two D -dimensional actions to be equal up to noncovariant field redefinitions, we find that both actions are fixed up to overall factors and up to field redefinitions.
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