7-dimensional 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). 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.