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du Bosque, Pascal; Hassler, Falk; Lüst, Dieter (2018): Generalized parallelizable spaces from exceptional field theory. In: Journal of High Energy Physics, No. 1, 117
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Abstract

Generalized parallelizable spaces allow a unified treatment of consistent maximally supersymmetric truncations of ten-and eleven-dimensional supergravity in generalized geometry. Known examples are spheres, twisted tori and hyperboloides. They admit a generalized frame field over the coset space M=G/H which reproduces the Lie algebra g of G under the generalized Lie derivative. An open problem is a systematic construction of these spaces and especially their generalized frames fields. We present a technique which applies to dim M=4 for SL(5) exceptional field theory. In this paper the group manifold G is identified with the extended space of the exceptional field theory. Subsequently, the section condition is solved to remove unphysical directions from the extended space. Finally, a SL(5) generalized frame field is constructed from parts of the left-invariant Maurer-Cartan form on G. All these steps impose conditions on G and H.