Geometry and fluxes of SL(5) exceptional field theory

Abstract

We use a geometric approach to construct a flux formulation for the SL(5) U-duality manifest exceptional field theory. The resulting formalism is well-suited for studying gauged supergravities with geometric and non-geometric fluxes. Here we describe all such fluxes for both M-theory and IIB supergravity including the Ramond-Ramond fields for compactifications to seven dimensions. We define the locally non-geometric "R-flux" and globally non-geometric "Q-flux" for M-theory and find a new locally non-geometric R-flux for the IIB theory. We show how these non-geometric fluxes can be understood geometrically and give some examples of how they can be generated by acting with dualities on solutions with geometric or field-strength flux.

Duality twisted reductions of Double Field Theory of Type II strings

“…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]. For recent work on how to truncate such theories further to half-maximal gauged supergravities, see [65,66].…”

Conserved currents of double field theory

“…It should not be difficult to calculate the current associated to the generalised diffeomorphisms which appear in an exceptional extended geometry [44,[69][70][71][72][73][74][75]. One reason this is interesting is that one will have duality transformations which map electric and magnetic solutions into each other (for instance, the M2 and M5).…”

“…This is unlike the case in T-duality, where we have argued that one needed different definitions of charge for electrical solutions like the F1 and magnetic solutions like the NS5. It is possible already to study the generalised fluxes of some of these exceptional field theories [75], and so it would be interesting to see what is contained additionally in the electrical current.…”

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

“…Originally developed in terms of an extended geometry [22][23][24][25][27][28][29][30] geometrising the E d(d) groups acting on a truncated d-dimensional theory, there is now a systematic method for constructing EFT in a form which is fully equivalent to the whole 11-or 10-dimensional supergravities [26]. So far EFTs have been developed for 3 ≤ d ≤ 8: E 8 [31], E 7 [32], E 6 [33], SO (5,5) [34], SL(5) [35] and SL(3) × SL(2) [36] theory, including the supersymmetrisation of the E 7 and E 6 cases [37,38].…”