7-dimensional N $$ \mathcal{N} $$ = 2 consistent truncations using SL(5) exceptional field theory

Abstract We show how to construct seven-dimensional half-maximally supersymmetric consistent truncations of 11-/10-dimensional SUGRA using SL(5) exceptional field theory. Such truncations are defined on generalised SU(2)-structure manifolds and give rise to seven-dimensional half-maximal gauged supergravities coupled to n vector multiplets and thus with scalar coset space ℝ + × O 3 , n / O 3 × O n $$ {\mathbb{R}}^{+}\times \mathrm{O}\left(3,\ n\right)/\mathrm{O}(3)\times \mathrm{O}(n) $$ . The consistency conditions for the truncation can be written in terms of the generalised Lie derivative and take a simple geometric form. We show that after imposing certain “doublet” and “closure” conditions, the embedding tensor of the gauged supergravity is given by the intrinsic torsion of generalised SU(2)-connections, which for consistency must be constant, and automatically satisfies the linear constraint of seven-dimensional half-maximal gauged supergravities, as well as the quadratic constraint when the section condition is satisfied