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Spheres, Generalised Parallelisability and Consistent Truncations
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DOI：10.1002/prop.201700048.png)
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Abstract
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We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a generalised parallelisation with a frame algebra with constant coefficients. The consistent truncation then arises as a generalised version of a conventional Scherk-Schwarz reduction with the frame algebra encoding the embedding tensor of the reduced theory. The key new result is that all round-sphere Sd geometries admit such generalised parallelisations with an SO(d+1) frame algebra. Thus we show that the remarkable consistent truncations on S-3, S-4, S-5 and S-7 are in fact simply generalised Scherk-Schwarz reductions. This description leads directly to the standard non-linear scalar-field ansatze and as an application we give the full scalar-field ansatz for the type IIB truncation on S-5.
Keywords:
Supergravity
Generalised geometry
Flux compactifications
Consistent truncations
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