Half‐Maximal Supersymmetry from Exceptional Field Theory

Abstract

We study D ≥ 4-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal Minkowski D and AdS D vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised SO(d−1−N ) structures, where d = 11−D, and N is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all D ≥ 4 half-maximal warped AdS D and Minkowski D vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a (6 + N )-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional N = 1 supergravity and another yielding six-dimensional N = (2, 0) SUGRA.

Duality twisted reductions of Double Field Theory of Type II strings

“…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].…”

Locally non-geometric fluxes and missing momenta in M-theory

“…As has already been argued in [43,[49][50][51][66][67][68][69], the tensor hierarchy of exceptional field theory defines a chain complex and its tensors can be thought of as the exceptional generalisation of differential forms. To capture the missing momenta, it seems likely that one should consider generalised vector fields V , since these contain two-forms, five-forms, etc., which are "closed" but not exact.…”

“…69) where the first line corresponds to the R-flux as already seen in five-dimensional compactifications, the second and third line represent modifications of the R-flux that first arose in six-dimensional compactifications and the final two locally non-geometric fluxes R and R ijkl are new and only arise in compactifications of seven or more dimensions. In fact, because seven-dimensional compactifications can depend on a Kaluza-Klein monopole winding number y i , there is a dual derivative ∂ i in the 7 of SL (7).…”

“…To answer this one could consider dualising a Kaluza-Klein monopole, which is a 1/2-BPS analogue of the Heisenberg Nilmanifold, in a similar way to the duality chains considered here. An efficient description of the duality chain may come by using the half-maximal structures in EFT [67][68][69]. Related to this, it would be interesting to try and find honest locally non-geometric M-theory backgrounds.…”

Supergravity Fluxes and Generalised Geometry

“…These results were established by showing that the Killing spinor equations precisely set the various components of the generalised intrinsic torsion to zero. [30,39] Descriptions of the conditions in terms of bosonic bilinears of the Killing spinors in the 8-supercharge and halfmaximal cases can be found also in [40][41][42][43].…”