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 \( {\mathbb{R}}^{+}\times \mathrm{O}\left(3,\ n\right)/\mathrm{O}(3)\times \mathrm{O}(n) \). 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.
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Malek, E. 7-dimensional \( \mathcal{N} \) = 2 consistent truncations using SL(5) exceptional field theory. J. High Energ. Phys. 2017, 26 (2017). https://doi.org/10.1007/JHEP06(2017)026
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DOI: https://doi.org/10.1007/JHEP06(2017)026