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.
Highlights
D U-d. group coord. irrep section condition (SC) irrep emb. tensor power of the EFT formalism, we try to understand these distinguished global symmetries from the eleven-dimensional perspective
If we switch on gaugings in the 40, we automatically reduce the dimension of the group manifold representing the extended space
We present a technique to explicitly construct the generalized frame fields for generalized parallelizable coset spaces M =G/H in four dimensions
Summary
Represents a generalized parallelization (1.3) of M. There are two choices of subgroups H which reproduce the duality chain four-torus with G- ↔ Q-flux [52] Another T-duality transformation results in a type IIB background with f - ↔ R-flux. This chain is captured by an embedding tensor solution in the 40. As an example for a physical manifold M without any non-contractible cycles, we discuss the four-sphere with G-flux For all these backgrounds we construct the generalized frame EA.
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