Double field theory on group manifolds

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.

T-duality and α′-corrections

“…Understanding the role of supersymmetry would also be of interest, since one should expect obstructions when attempting to supersymmetrize this theory for a choice of parameters leaving only even Z 2 -parity corrections. Generalized Scherk-Schwarz reductions like those considered in [47,48] would also be interesting to examine in order to find higher-derivative corrections in gauged supergravities and to clarify the relation between α ′ -corrections and non-geometry (see for example [49][50][51][52][53][54][55] and references therein). Due to the field redefinitions involved in this construction, we expect the duality covariant scalars of the reduced theory to be related to the diffeomorphism and Lorentz covariant scalars through O(α ′ ) redefinitions that are quadratic in gaugings.…”

On the exceptional generalised Lie derivative for d ≥ 7

“…The strong constraint can be locally relaxed [12][13][14]. Some works in the direction of understanding, from the world sheet perspective, the origin of the strong constraint and its possible relaxation have appeared in the literature [15][16][17]. However, the geometric interpretation of this relaxed theory is still not clear.…”

The bosonic string on string-size tori from double field theory

“…the vielbein (4.23) gives the desired g × g algebra [9,[14][15][16]. We now show that this vielbein also satisfies the assumption (4), namely the generalized metric when restricted to the Cartan subsector reduces to that of the torus.…”

“…The deformation accounts for the cocycle factors that are necessary in the vertex representation of the current algebra, and then we can reproduce the g×g algebra with a generalized vielbein that depends on k+k coordinates only. An alternative generalized frame can be constructed from the formulation of DFT on group manifolds [14,16], in which it depends on n coordinates. The question whether there exists a vielbein depending strictly on k + k coordinates that gives rise to the g × g algebra under the usual C-bracket, when g has at least one non-simple root, remains open.…”

“…An alternative construction of the generalized internal vielbein can be obtained from the formulation of DFT on group manifolds [14,16] if the fifth condition in section 4.2 is relaxed and one allows the vielbein to depend on coordinates beyond the torus ones and their duals. In this framework, the vielbein depends on the n coordinates of the group manifold corresponding to one of the factors of the enhanced symmetry group.…”