Spheres, Generalised Parallelisability and Consistent Truncations
By Kanghoon Lee, C. Strickland-Constable, D. Waldram. 2014
210 citations recorded by the source corpus.
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 S3, S4, S5 and S7 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 S5.
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Citations in the corpus
- Consistent Kaluza-Klein truncations via exceptional field theory (2014, methodology): “raints are automatically satised as a consequence of the section constraints (2.1). 5It is in this ‘SLpnqgeneralized geometry’ that the generalized parallelizability of spheres has been discussed in [38]. 19 in terms of an SLpnq-valued n ntwist matrix U A B. For D7 maximal supergravity, the embeddin”