Half-maximal consistent truncations using exceptional field theory

We show how to construct half-maximal consistent truncations of 10- and 11-dimensional supergravity to seven dimensions using exceptional field theory. This procedure gives rise to a seven-dimensional half-maximal gauged supergravity coupled to $n$ vector multiplets, with $n\mathrm{\ne }3$ in general. We also show how these techniques can be used to reduce exceptional field theory to heterotic double field theory.