Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions

Abstract

We consider the reduction of the duality invariant approach to Mtheory by a U-duality group valued Scherk-Schwarz twist. The result is to produce potentials for gauged supergravities that are normally associated with non-geometric compactifications. The local symmetry reduces to gauge transformations with the gaugings exactly matching those of the embedding tensor approach to gauged supergravity. Importantly, this approach now includes a nontrivial dependence of the fields on the extra coordinates of the extended space.

Duality twisted reductions of Double Field Theory of Type II strings

“…Therefore, the existence of this extra constraint can be seen as a sign that the reduction we have studied here should be related to duality twisted reductions of Exceptional Field Theory (EFT), which is a U-duality invariant extension of supergravity [56][57][58][59]. Indeed, the reduction of EFT on generalised parallelisable manifolds [60] (which corresponds to a reduction with a duality twisted anzats of the type we have considered here) gives rise to maximal gauged supergravity upon imposing a section constraint, which is the analogue of the strong constraint of DFT [61][62][63]. A flux formulation of (a particular type of) EFT is also available and geometric and non-geometric RR fluxes were studied also in this formulation [64].…”

Extended geometry and gauged maximal supergravity

“…In the case of constant fluxes, the generalized Ricci scalar is exactly equal to the potential of N = 8 supergravity, provided we identify the generalized metric with the moduli space metric for the N = 8 scalars. Some definitions and results for d < 6 are given in [27], and some more for d = 4, 5 in [42]. Finally, for completion we provide a list of complementary results along these lines [43][44][45]- [51].…”

U-duality covariant gravity

“…In addition, we will have to introduce extra fields and constraints, but the extra fields can be eliminated once the constraints are solved. After the advent of DFT, there have already been quite a number of papers extending the techniques developed here to various U-duality groups [45][46][47][48][49][50][51] (see also [52,53] for earlier results). The actions given in this context exhibit manifest E n(n) symmetry for n ≤ 7 and describe truncations of D = 11 supergravity.…”