Abstract
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
Highlights
Standard dualizationsAs a warm-up we start by recalling the dualization of the electromagnetic field in four dimensions
For a p-form potential, this dualization is straightforward: one replaces its (p + 1)-form field strength by the Hodge-dual of the field strength of the dual (D − p − 2)form
We present the dual formulation of double field theory at the linearized level
Summary
As a warm-up we start by recalling the dualization of the electromagnetic field in four dimensions. Where Fab = 2∂[aAb], one moves to a first-order formulation where Fab is an independent field, and the Bianchi identity is imposed by introducing a Lagrange multiplier Aa, S[A, F ] =. This action is gauge invariant under δAa = ∂aΛ, δFab = 0. In order to set the stage for the comparison with the dualization in DFT, we will often consider the Hodge duals of the potential AD−p−2 and the gauge parameter ΛD−p−3. Consider a 2-form b2 in D dimensions with field strength Habc = 3∂[abbc]. We pass to a first order action with a fully antisymmetric 4-tensor Dabcd and 3-form Habc as independent fields, S[D, H] =.
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