F-term uplifting and moduli stabilization consistent with Kahler invariance

TL;DR

This paper addresses the challenge of uplifting AdS supersymmetric moduli to Minkowski or de Sitter vacua without destabilizing the minimum. It introduces an F-term uplifting construction that preserves supersymmetric critical points and shift symmetries by coupling two sectors through an additive Kähler function, yielding a total potential $V = e^{A+B}\bigl[ A^{\alpha\bar{\beta}} A_\alpha A_{\bar{\beta}} + B^{i\bar{j}} B_i B_{ar{j}} - 3 \bigr]$. A key result is that the stability of uplifted points depends only on two parameters, $b = B^{i\bar{j}} B_i B_{ar{j}}$ and $x = \left|\frac{A_{zz}}{A_{z\bar{z}}}\right|$, with Minkowski uplift ($b=3$) guaranteeing stability for all SUSY critical points, while larger $b$ supports de Sitter vacua. The analysis is carried out in a toy one-modulus model, where cross-couplings vanish at the critical point and stability reduces to independent sector checks, and is further enriched by discussing shift symmetries and effective field theory implications. Overall, the work provides a principled, Kähler-invariant pathway to F-term uplifting with controlled moduli stabilization and potential inflationary directions.

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 {\em maxima} --or, more importantly, local minima of the Kahler 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.

Figures (1)

• Figure 1: Stability of critical points after uplifting to Minkowski ($b=3$) or de Sitter ($b>3$) in the toy model described in the text. The shaded areas indicate stability along the moduli $z$ directions. The vertical axis shows the quantity $b-3=e^{-G} V/M_p^4$ evaluated at the critical point, which represents the amount of uplifting. The horizontal axis shows the value of the quantity $|x|= |G_{zz}/G_{z\bar{z}}||_{z=z_0}$ at the critical point. Local minima before uplifting $(|x|>2)$ become unstable for sufficiently large upliftings. By contrast, local maxima before uplifting $(|x|<1)$ become more stable with increasing uplifting.