Abstract
Exceptional generalised geometry is a reformulation of eleven/ten-dimensional supergravity that unifies ordinary diffeomorphisms and gauge transformations of the higher-rank potentials of the theory in an extended notion of diffeormorphisms. These features make exceptional generalised geometry a very powerful tool to study consistent truncations of eleven/ten-dimensional supergravities. In this article, we review how the notion of generalised G-structure allows us to derive consistent truncations to supergravity theories in various dimensions and with different amounts of supersymmetry. We discuss in detail the truncations of eleven-dimensional supergravity to N=4 and N=2 supergravity in five dimensions.
Highlights
We will briefly discuss the example of the generalised Scherk–Schwarz reduction and show how this approach allows us to prove the conjecture of [25] that any supersymmetric solution to ten/elevendimensional supergravity that is a warped product of AdSD × M admits a consistent truncation to pure gauged supergravity in D dimensions containing that solution and having the same amount of supersymmetry
We showed that in order to have a consistent truncation of a given supergravity theory on a manifold M, this must admit a generalised GS -structure with singlet intrinsic torsion
We focussed on eleven-dimensional supergravity, and we studied in detail the truncations to N = 4 and N = 2 five-dimensional supergravity
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [23], it was proved that given a manifold M admitting a generalised GS -structure with singlet intrinsic torsion, a consistent truncation of any field theory on M is obtained by expanding all the fields on the GS invariant tensors and keeping only those transforming as singlets In this language, all maximally supersymmetric truncations correspond to generalised parallelisable manifolds, namely to a generalised identity structure, while truncations preserving less supersymmetry are based on generalised structures larger than the identity. We will briefly discuss the example of the generalised Scherk–Schwarz reduction and show how this approach allows us to prove the conjecture of [25] that any supersymmetric solution to ten/elevendimensional supergravity that is a warped product of AdSD × M admits a consistent truncation to pure gauged supergravity in D dimensions containing that solution and having the same amount of supersymmetry. Rather than describing explicit examples of truncations, which can be found in [23,24], we will discuss the general procedure and how the data of the GS -structure on the internal manifold are mapped onto those of the truncated theory
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