The Embedding of Gauged STU Supergravity in Eleven Dimensions
Arash Azizi, Hadi Godazgar, Mahdi Godazgar, C.N. Pope

TL;DR
This paper provides explicit embedding formulas for reducing four-dimensional gauged supergravity theories, specifically the N=2 STU model, into eleven-dimensional supergravity, facilitating the uplift of complex black hole solutions.
Contribution
The paper derives explicit expressions for embedding N=2 gauged STU supergravity into eleven-dimensional supergravity, extending previous work on the full N=8 theory.
Findings
Explicit embedding formulas for N=2 STU supergravity into 11D supergravity.
Simplified truncations to N=2 supergravities with fewer vector multiplets.
Enabling uplift of 8-charge black hole solutions to eleven dimensions.
Abstract
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…
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