Abstract
Double Field Theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of $\alpha'$ is invariant under global $O(D,D)$ transformations and ought to be invariant under gauge transformations which receive $\alpha'$-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 $\alpha'$-corrections. We speculate that the combination of these two constraints may fix both the $2D$-dimensional and the $D$-dimensional effective actions without knowledge of the $\alpha'$-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 $\alpha'^0$ and $\alpha'$, 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 non-covariant field redefinitions, we find that both actions are fixed up to overall factors and up to field redefinitions.
Highlights
One of the most exciting discoveries in string theory is T-duality [1,2]
The double field theory (DFT) is a constraint field theory which doubles the spacetime coordinates, i.e., adds to the usual D-dimensional spacetime coordinates which correspond to the momentum excitations, another D-dimensional coordinates which correspond to the winding excitations
Since the field redefinitions freedom is not fixed in the 2D-dimensional action, we have found the 2D-dimensional action with some arbitrary parameters
Summary
One of the most exciting discoveries in string theory is T-duality [1,2]. This duality may be used to construct the effective field theory at low energy. Another T-duality based approach for constructing the effective action at higher orders of α0, is to use the constraint that the dimensional reduction of the effective action on a circle must be invariant under the T-duality transformations [12] In this approach, one begins with the most general gauge invariant action in the D-dimensional spacetime. (2) After reducing it to the D-dimensional spacetime and using noncovariant field redefinitions, the action is constrained to be the same as a D-dimensional action which is invariant under the standard coordinate transformations, the B-field gauge transformations and the nonstandard Lorentz transformation of the B-field, it is not invariant under the T-duality transformations which receive α0-corrections. Using the generalized fluxes, we first construct the most general OðD; DÞ-invariant action at order α0 without fixing its field redefinitions freedom, and reduce it to the D-dimensional action. In one particular scheme in which dilaton appears as an overall factor, we write the effective action
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