More about<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math>-term uplifting

Abstract

We study moduli stabilization and a realization of de Sitter vacua in generalized $F$-term uplifting scenarios of the Kachru-Kallosh-Linde-Trivedi--type anti--de Sitter vacuum, where the uplifting sector $X$ directly couples to the light K\"ahler modulus $T$ in the superpotential through, e.g., stringy instanton effects. $F$-term uplifting can be achieved by a spontaneous supersymmetry breaking sector, e.g., the Polonyi model, the O'Raifeartaigh model, and the Intriligator-Seiberg-Shih model. Several models with the $X\mathrm{\text{\ensuremath{-}}}T$ mixing are examined, and qualitative features in most models even with such mixing are almost the same as those in the Kachru-Kallosh-Linde-Trivedi scenario. One of the quantitative changes, which are relevant to the phenomenology, is a larger hierarchy between the modulus mass ${m}_{T}$ and the gravitino mass ${m}_{3/2}$, i.e., ${m}_{T}/{m}_{3/2}=\mathcal{O}({a}^{2})$, where $a\ensuremath{\sim}4{\ensuremath{\pi}}^{2}$. In spite of such a large mass, the modulus $F$ term is suppressed not like ${F}^{T}=\mathcal{O}({m}_{3/2}/{a}^{2})$, but like ${F}^{T}=\mathcal{O}({m}_{3/2}/a)$ for $\mathrm{ln}({M}_{\mathrm{Pl}}/{m}_{3/2})\ensuremath{\sim}a$, because of an enhancement factor coming from the $X\mathrm{\text{\ensuremath{-}}}T$ mixing. Then we typically find a mirage-mediation pattern of gaugino masses of $\mathcal{O}({m}_{3/2}/a)$, while the scalar masses would be generically of $\mathcal{O}({m}_{3/2})$.