Consistent Truncations and Generalised Geometry: Scanning through Dimensions and Supersymmetry

TL;DR

This work develops a unifying framework, based on Exceptional Generalised Geometry, to classify four-dimensional gauged supergravities that can arise as consistent truncations of 10/11-dimensional supergravity. By reducing to a generalised G_S-structure with constant singlet intrinsic torsion, the authors derive the full field content, supersymmetry, and possible gaugings for each admissible truncation, with the embedding tensor identified with the singlet intrinsic torsion. The paper achieves a complete classification for all continuous G_S structures and provides detailed accounts of the resulting N≥2 theories, including several known truncations and new possibilities, together with a parallel review of truncations to five, six and seven dimensions. The results illuminate the geometric and group-theoretic fingerprints of consistent truncations, offering a systematic path to construct uplifts and to study AdS/CFT-related vacua and black-hole solutions in a broad swath of dimensions. The methodology paves the way for further exploration of discrete G_S structures, explicit higher-dimensional realizations, and extensions to lower-supersymmetry truncations, with potential applications to holography and quantum gravity embeddings via $E_{7(7)}$ geometry.

Abstract

We study consistent truncations in the framework of Exceptional Generalised Geometry. We classify the 4-dimensional gauged supergravities that can be obtained as a consistent truncation of 10/11-dimensional supergravity. Any truncation is associated to a (generalised) $G_S$-structure with singlet intrinsic torsion. We give the full classification for all truncations associated to continuous structure groups and we discuss a few examples with discrete ones. We recover gauged supergravities corresponding to known truncations as well as others for which explicit truncations are still to be constructed. We also summarise similar results obtained in the literature for truncations to $d=5,6,7$ dimensions and we complete them, when needed.