F-term uplifting and moduli stabilization consistent with Kähler invariance

Abstract

An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite of a direct coupling, the moduli do not contribute to supersymmetry breaking. We analyse the stability of the critical points in a toy one-modulus sector before and after uplifting, and find a simple stability condition depending solely on the amount of uplifting and not on the details of the uplifting sector. There is a region of parameter space, corresponding to the uplifting of local AdS maxima -or, more importantly, local minima of the Kähler function-where the critical points are stable for any amount of uplifting. On the other hand, uplifting to (non-supersymmetric) Minkowski space is special in that all SUSY critical points, that is, for all possible compactifications, become stable or neutrally stable.

Universal properties of type IIB and F-theory flux compactifications at large complex structure

“…Including such interactions will generically affect the spectra, unless the additional sectors can be integrated out or consistently truncated while preserving supersymmetry [19][20][21][22][23][24][25]. In string compactifications, the form of the interactions with the Kähler sector is partly determined by the corresponding moduli stabilisation mechanism, which we here don't specify.…”

Inflation and String Theory

“…44 Unbroken supersymmetry in AdS does not guarantee the absence of tachyons allowed by the Breitenlohner-Freedman bound [475], but the techniques described above can be used to compute the probability that there are no tachyons [476]. See also [477]. 45 The principal instability corresponds to the scalar partner of the Goldstino -see [478] for an analysis of geometric conditions that ensure stability in this direction, and [479,480] for discussions of inflation along this direction.…”

D 3 ¯ $$ \overline{D3} $$ induced geometric inflation

“…For these models it was more useful to employ the Kähler potential and the superpotential W since the Kähler function G has a singularity at W = 0. Meanwhile, the analysis of non-supersymmetric Minkowski and metastable de Sitter vacua with spontaneously broken supersymmetry was based mostly on the analysis using the Kähler function G, see for example, [33][34][35][36][37]. Comparative to this analysis, the new ingredient here is the fact that the S superfield is nilpotent and that we will use it for developing inflationary models with the exit to de Sitter minima.…”

“…The scalar potential is 34) and the last term gives the dynamical constraint φ i = φ j where we have defined canonical fields as…”