More about F-term uplifting

TL;DR

This paper extends KKLT-style moduli stabilization by incorporating generalized F-term uplifting with direct X–T coupling in the nonperturbative superpotential. Through Polonyi-KKLT, ISS-KKLT, and ISS-racetrack constructions, it demonstrates that the qualitative KKLT-like vacuum structure is robust to X–T mixing, while revealing a pronounced increase in the modulus-to-gravitino mass ratio, $m_T/m_{3/2} = {\cal O}(a^2)$. Importantly, the modulus F-term remains suppressed at $F^T = {\cal O}(m_{3/2}/a)$ due to the enhancement from X–T mixing, leading to mirage-type gaugino masses $\mathcal{O}(m_{3/2}/a)$ with scalar masses typically $\mathcal{O}(m_{3/2})$. The work also identifies model-dependent phenomenology, including the anomaly/modulus mediation ratio $\alpha$ spanning order-one values to larger magnitudes in ISS-racetrack variants, and discusses implications for inflationary stability and potential cosmological constraints.

Abstract

We study moduli stabilization and a realization of de Sitter vacua in generalized F-term uplifting scenarios of the KKLT-type anti-de Sitter vacuum, where the uplifting sector X directly couples to the light Kähler 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-T mixing are examined and qualitative features in most models {\it even with such mixing} are almost the same as those in the KKLT 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., $m_T/m_{3/2} = {\cal O}(a^2)$, where $a \sim 4 π^2$. In spite of such a large mass, the modulus F-term is suppressed not like $F^T = {\cal O}(m_{3/2}/a^2)$, but like $F^T = {\cal O}(m_{3/2}/a)$ for $\ln (M_{Pl}/m_{3/2}) \sim a$, because of an enhancement factor coming from the X-T mixing. Then we typically find a mirage-mediation pattern of gaugino masses of ${\cal O}(m_{3/2}/a)$, while the scalar masses would be generically of ${\cal O}(m_{3/2})$.