The higher-dimensional origin of five-dimensional $\boldsymbol{{\cal N}\!=\!2}$ gauged supergravities

TL;DR

This paper classifies five-dimensional ${ m f N}=2$ gauged supergravities that can be derived from higher-dimensional supergravity using exceptional generalised geometry, focusing on algebraic subgroup structures and intrinsic torsion conditions.

Contribution

It provides a systematic algebraic classification of five-dimensional ${ m f N}=2$ gauged supergravities from 10-/11-dimensional supergravity via exceptional generalised geometry, including constraints on scalar manifolds and matter content.

Findings

Scalar manifolds are symmetric spaces.

Limited matter multiplets can be retained.

Largest gaugings from consistent truncations are identified.

Abstract

Using exceptional generalised geometry, we classify which five-dimensional ${\cal N}=2$ gauged supergravities can arise as a consistent truncation of 10-/11-dimensional supergravity. Exceptional generalised geometry turns the classification into an algebraic problem of finding subgroups $G_S \subset \mathrm{USp}(8) \subset \mathrm{E}_{6(6)}$ that preserve exactly two spinors. Moreover, the intrinsic torsion of the $G_S$ structure must contain only constant singlets under $G_S$, and these, in turn, determine the gauging of the five-dimensional theory. The resulting five-dimensional theories are strongly constrained: their scalar manifolds are necessarily symmetric spaces and only a small number of matter multiplets can be kept, which we completely enumerate. We also determine the largest reductive and compact gaugings that can arise from consistent truncations.