F-term uplifting and the supersymmetric integration of heavy moduli

Abstract

We study in detail the stability properties of the simplest F-term uplifting mechanism consistent with the integration of heavy moduli. This way of uplifting vacua guarantees that the interaction of the uplifting sector with the moduli sector is consistent with integrating out the heavy fields in a supersymmetric way. The interactions between light and heavy fields are characterized in terms of the Kahler invariant function, G = K + log |W|^2, which is required to be separable in the two sectors. We generalize earlier results that when the heavy fields are stabilized at a minimum of the Kahler function G before the uplifting (corresponding to stable AdS maxima of the potential), they remain in a perturbatively stable configuration for arbitrarily high values of the cosmological constant (or the Hubble parameter during inflation). By contrast, supersymmetric minima and saddle points of the scalar potential are always destabilized for sufficiently large amount of uplifting. We prove that these results remain unchanged after including gauge couplings in the model. We also show that in more general scenarios, where the Kahler function is not separable in the light and heavy sectors, the minima of the Kahler function still have better stability properties at large uplifting than other types of critical points.

Figures (1)

• Figure 1: Stability of supersymmetric critical points after the uplifting. The quantity on the vertical axis $b-3$ is proportional to the cosmological constant (or the Hubble parameter during inflation). The horizontal axis represents the curvature of the Kähler function at the critical point along one of the heavy field directions $H^\alpha$: $|x_\lambda|<1$ corresponds to local minima and $|x_\lambda|>$ to saddle points. The shaded region represents stable configurations under perturbations of the heavy fields. For $b<3$ and $b=3$ the uplifted vacua, which are AdS and Minkowski respectively, are always stable. Local AdS minima of the scalar potential at zero uplifting, $|x_\lambda|>2$, are always destabilized for large uplifting. Local AdS maxima, $|x_\lambda|<1$, remain stable for arbitrary large uplifting.