All maximal gauged supergravities with uplift

Abstract

Abstract Generalized parallelizable spaces permit the uplift of many maximal gauged supergravities to ten or eleven dimensions. Although some of the former are explicitly known, the literature is still lacking their systematic construction. We resolve this issue by going beyond the known existence proofs and present the explicit construction of all generalized parallelizable spaces for maximal gauged supergravities in four or more dimensions. In the process, all embedding tensors that can be realized without breaking the section condition of exceptional field theory are identified. This addresses the old question: “Which maximal gauged supergravities can be embedded in the low-energy limit of superstring/M-theory” and provides the basis to explore solution-generating techniques based on generalized dualities.