$O(D,D)$-constraint on $D$-dimensional effective actions

Abstract

Double Field Theory is a manifestly T-duality invariant formulation of string theory in which the effective theory at any order of ${\alpha }^{\prime }$ is invariant under global $O(D,D)$ transformations and ought to be invariant under gauge transformations which receive ${\alpha }^{\prime }$-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 ${\alpha }^{\prime }$-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 ${\alpha }^{\prime }$-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 ${\alpha }^{\prime 0}$ and ${\alpha }^{\prime }$, 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.

18 pages, Latex file, no figure; v2: field redefinitions between 2D- and D-dimensional actions are added,v3: the version appears in PRD

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• Double Field Theory
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Cited by in corpus (3)

• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint