Embedding of gauged STU supergravity in eleven dimensions

The consistency of the embedding of four-dimensional SO(8) gauged 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 N = 8 gauged theory to the N = 2 gauged STU supergravity. This corresponds, in the bosonic sector, to a consistent truncation of the 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 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 N = 2 supergravities coupled to single vector multiplets.