The effective theory of type IIA AdS ₄ compactifications on nilmanifolds and cosets

Abstract

We consider string theory compactifications of the form AdS 4 ×M 6 with orientifold six-planes, where M 6 is a six-dimensional compact space that is either a nilmanifold or a coset. For all known solutions of this type we obtain the four-dimensional N = 1 low energy effective theory by computing the superpotential, the Kähler potential and the mass spectrum for the light moduli. For the nilmanifold examples we perform a cross-check on the result for the mass spectrum by calculating it alternatively from a direct Kaluza-Klein reduction and find perfect agreement. We show that in all but one of the coset models all moduli are stabilized at the classical level. As an application we show that all but one of the coset models can potentially be used to bypass a recent no-go theorem against inflation in type IIA theory.

Towards Kaluza-Klein Dark Matter on nilmanifolds

“…Four-dimensional gauged supergravities can be obtained by a truncation to a finite set of modes, as e.g. in [40,41]. Whether this set corresponds to the light modes in a controlled low-energy approximation has not yet been settled.…”

Warped generalized geometry compactifications, effective theories and non‐perturbative effects

“…where j np is the generalized current for the cycle wrapped by the instantons or the Dbranes on which the gaugino condensation takes place, and the overall factor A comes from the determinant of the Dirac action for the fermions on the D-branes, and should depend holomorphically on the background closed and open string degrees of freedom in a way consistent with the complexified Weyl invariance (12,13), which becomes the Kähler invariance in the Einstein frame. Its explicit form is generically hard to compute.…”

“…This full reduction, which would be the next step, would involve making a choice of suitable zero-or light modes in which to expand and would depend on the details of the compactification [11,12,13]. However, it turns out that we can already gain new insights in the current description, for instance when adding a non-perturbative superpotential, a quantity usually associated to the four-dimensional description, as we will demonstrate in section 3.…”

Nearly‐Kähler dimensional reduction of the heterotic string

“…A third contribution to the Kähler potential due to the complex structure moduli is not present here since the SU(3)-structures we consider are real. Applying (12) to the cases of G 2 /SU(3), Sp 4 /(SU(2) × U(1)) non−max and SU(3)/U(1) × U(1) respectively, the corresponding superpotentials take the form…”