Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10

Abstract

Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S^7 from D=11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable, for the purposes of lifting lower-dimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansatze comes from the spin-0 fields, and of these, it is the pseudoscalars that are the most difficult to handle. In this paper we address this problem in two cases. One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1)^4, where there are three pairs of dilatons and axions in the scalar sector. The other example involves the truncation of SO(6) gauged supergravity in D=5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximally-supersymmetric one. We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.

Latex, 24 pages, typos corrected

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• The Kahler Structure of Supersymmetric Holographic RG Flows
• Susy Q and spatially modulated deformations of ABJM theory
• The Embedding of Gauged STU Supergravity in Eleven Dimensions
• Gauged Supergravities from Spherical Reductions
• AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model
• Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy
• Consistent 4-form fluxes for maximal supergravity
• Towards New Membrane Flow from de Wit-Nicolai Construction
• Separability in Consistent Truncations