Abstract
A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.
Highlights
Double Field Theory (DFT) is an approach along these lines [1,2,3,4,5,6,7]
A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric Wess-ZuminoWitten model (WZW) model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order
DFT was derived from Closed String Field Theory (CSFT) expanding it up to cubic order on a torus1 [2]
Summary
We briefly review the WZW model and its current algebra providing the notation for the rest of the paper. For a more detailed review of WZW models, we refer to e.g. [36] or the appendix of [37]. We show how the various representations of a semisimple Lie algebra can be expressed in terms of scalar functions on the group manifold. Afterwards, we use this result to express two- and three-point correlators and show that they fulfill the Knizhnik-Zamolodchikov equation [38]. We provide the two- and three-point off-shell amplitude for Kac-Moody primary fields
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