F-term uplifting and moduli stabilization consistent with Kähler invariance

TLDR: In this article, a variant of F-term uplifting is proposed, which exactly preserves supersymmetric critical points and shifts symmetries at tree level, and finds a simple stability condition depending solely on the amount of uplifting.

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 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.