The Embedding of Gauged STU Supergravity in Eleven Dimensions

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 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-AdS rotating black holes to eleven dimensions. We also give two distinct further truncations to N=2 supergravities coupled to single vector multiplets.