How to uplift non-maximal gauged supergravities

A bstract In this paper, we provide an algorithm to perform the uplift of non-maximal G g -gauged supergravities to type IIB or 11D supergravities. Using tools of exceptional field theory and generalised geometry, we show that the internal manifold admits a G g -action, and that consistency of the uplift is equivalent to solving a simpler PDE on the quotient M int / G g . As an application, we classify all possible uplifts of pure half-maximal four-dimensional SO(4)-gauged supergravity to type IIB and we recover consistent truncations around any of the D’Hoker-Estes-Gutperle solutions [ JHEP 06 (2007) 022].