Generalized parallelizable spaces from exceptional field theory

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.

Exotic branes in Exceptional Field Theory: the SL(5) duality group

“…These are fascinating global questions. In [92,93,94,95] these global questions were addressed and various proposals made for DFT. A clear input (especially in [93,94]) was from the study of so called topological T-duality of the type studied in [96].…”

U -duality extension of Drinfel’d double

“…For this purpose, we need to extend the exceptional space to some extended group manifold, similar to the Drinfel'd double. Such an extension has been studied in [59], but the relation to the Drinfel'd double is not so clear and no proposal has been made for the extension of the PL T -duality.…”

Doubled aspects of generalised dualities and integrable deformations

“…A pivotal element in our discussion will be a generalised frame field on the spacetime which allows us to connect the fields on the doubled space with the conventional type II supergravity fields. In this work we will follow a technique suggested in [45] to construct a set of O(D, D) valued generalised frame fields that furnish the algebra of D via the generalised Lie derivative. In the cases we are most interested in, and that includes η-, λ-and β-deformations as well as all PL dualisable models, this construction is carried out explicitly making use of the group theoretic quantities on D and its coset M = D/ H by a maximal isotropic subgroup H. Our discussion will be predominantly local in nature, however where this construction can be extended globally this provides an understanding of E-models as examples of generalised parallelizable spaces [46,47].…”