Gauged double field theory

Abstract

We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but not necessary. We then analyze compactifications of DFT on twisted double tori satisfying the consistency conditions. The effective theory is a Gauged DFT where the gaugings come from the duality twists. The action, bracket, global symmetries, gauge symmetries and their closure are computed by twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic string and lower dimensional gauged supergravities are particular examples of Gauged DFT.

Doubled α ′-geometry

“…The RamondRamond sector of type-II superstrings is given in [31,32], and its supersymmetric extension in [33]. Double field theory formulations where the strong constraint is somewhat relaxed have been given for massive IIA supergravity in [29], for flux compactifications in [37,38], and explored in some generality in [39,40]. See also [41,42] for the geometric role of nongeometric fluxes in double field theory.…”

Extended geometry and gauged maximal supergravity

“…Nevertheless, by an abuse of notation we will still call these fluxes, and we will call Ω in (2.12) the Weitzenböck connection. Rotating these expressions with the bein we can define the fluxes with curved indices 13) and the corresponding Weitzenböck connection in curved indices…”

“…In [12,13] it was shown that the section condition is sufficient for the gauge consistency of the theory, but not necessary. Rather, in particular setups such as the ones discussed below, it is not hard to see that the constraints (3.9) and (3.12) are weaker than the strong constraint, and this allows for extended configurations not solving the section condition.…”

“…The torsionless (4.6) and the trace equations (4.12) imply that the connection takes the form 13) whereΓ belongs to the 6480 of 56 × 133 (which is traceless). This piece remains undetermined here, but a part of it will be fixed by imposing metric compatibility.…”

On the exceptional generalised Lie derivative for d ≥ 7

“…This implies that they depend on only ten coordinates and, therefore, locally DFT is equivalent to generalised geometry. 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].…”