Consistent truncation of d = 11 supergravity on AdS_4 x S^7

Abstract

We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.

41 pages, typos corrected, published version

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• Generalised geometry from the ground up
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• Mass Deformations of the ABJM Theory: The Holographic Free Energy
• On the moduli space of spontaneously broken N = 8 supergravity
• The complete $D=11$ embedding of SO(8) supergravity
• A new N=1 AdS4 Vacuum of Maximal Supergravity
• $\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory
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• S-folds and holographic RG flows on the D3-brane
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• Einstein-Cartan Calculus for Exceptional Geometry
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• Rotating D0-branes and consistent truncations of supergravity
• Gaugings from E7 Extended Geometries
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• Consistent truncations in higher derivative supergravity
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• Observables in the Guarino-Jafferis-Varela/CS-SYM duality
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