Double Field Theory on Group Manifolds

TL;DR

This paper extends double field theory to group manifolds using asymmetric WZW models, revealing new structures like a background-dependent covariant derivative and insights into non-geometric reductions.

Contribution

It derives a generalized DFT for group manifolds from WZW models, introducing a background-dependent covariant derivative and a new strong constraint.

Findings

Derived DFT action and gauge transformations for group manifolds.

Identified a background-dependent covariant derivative reducing to partial derivatives on tori.

Revealed a generalized Lie derivative and C-bracket in this framework.

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.