Consistent truncations of M-theory for general SU(2) structures

In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give the relation of SU(2) torsion classes and fluxes to gaugings in the N=4 theory. We furthermore show explicitly that this reduction is a consistent truncation of the eleven-dimensional theory, in other words classical solutions of the reduced theory also solve the eleven-dimensional equations of motion. This reduction generalizes previous M-theory reductions on Tri-Sasakian manifolds and type IIA reductions on Calabi-Yau manifolds of vanishing Euler number. Moreover, it can also be applied to compactifications on certain G2 holonomy manifolds and to more general flux backgrounds.