The consistency of the embedding of four-dimensional $SO(8)$ gauged $\mathcal{N}=8$ supergravity into eleven-dimensional supergravity, where the internal directions are compactified on a seven-sphere, was established by de Wit and Nicolai in the 1980s. The reduction Ansatz for the eleven-dimensional metric, and for some of the components of the 4-form field strength, were found at that time, and recently the complete expression for the 4-form reduction has been obtained. The expressions are quite complicated, and in many practical applications it would be sufficient to know the Ansatz for a subset of the four-dimensional fields. In this paper, we obtain explicit expressions for the embedding of the truncation of the full $\mathcal{N}=8$ gauged theory to the $\mathcal{N}=2$ gauged STU supergravity. This corresponds, in the bosonic sector, to a consistent truncation of the $\mathcal{N}=8$ supergravity fields to those that are singlets under the $U(1{)}^4$ Cartan subalgebra of $SO(8)$. This truncation to STU supergravity, which comprises $\mathcal{N}=2$ supergravity coupled to three vector multiplets, suffices, for example, for lifting the general 8-charge asymptotically anti–de Sitter rotating black holes to eleven dimensions. We also give two distinct further truncations to $\mathcal{N}=2$ supergravities coupled to single vector multiplets.

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• Classical black holes
• Gauge-gravity dualities
• Supergravity