Abstract
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.
Highlights
For these compactifications and lead to the conjecture that certain non-perturbative string corrections must vanish for these backgrounds
In seven dimensions any spin manifold admits an SU(2) structure and very general M-theory compactifications have the potential to allow for a reduction to N = 4 gauged supergravity
We show explicitly that this reduction is a consistent truncation of the eleven-dimensional theory, in other words classical solutions of the reduced theory solve the eleven-dimensional equations of motion
Summary
The almost product structure (2.7) on Y will play a central role in the choice of our reduction ansatz. We can expand the three-form gauge field in terms of this basis Note that the flux piece in (3.9) proportional to vol4(Mink) can be absorbed in dCbut will reoccur later when we introduce dual fields. We discuss this seven-form flux again in appendix B.1. The coefficients tab, taI and TaIJ are constants that parameterize the SU(2) structure reduction ansatz for a particular manifold. Note that in the second equation of (3.15) a possible term proportional to v1 ∧ v2 ∧ v3 is immediately set to zero by the constraint that d(ωI ∧ ωJ ∧ ωK ) = 0. The tab, taI and TaIJ specify the torsion classes of Y. If tab is non-zero, the taI form a non-trivial representation under S.
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