Effective potentials, warping, and implications for F-term uplifting

TL;DR

This paper investigates warping effects on the scalar potential in Type IIB flux compactifications, revealing their significant impact on F-term de Sitter uplifting and the controllability of KKLT and LVS models.

Contribution

It derives a systematic off-shell potential considering warping and fluxes, proposes a warped Kähler potential, and compares effects in KKLT and LVS frameworks.

Findings

Warping corrections dominate in KKLT, making the scenario uncontrollable.

In LVS, corrections are suppressed by inverse powers of volume, improving control.

Classical warping and flux effects significantly influence de Sitter uplifting scenarios.

Abstract

We analyse warping corrections to the scalar potential in flux compactifications of Type IIB string theory, focusing on their effect on $F$-term de Sitter uplifting in Calabi-Yau orientifold models. A systematic inverse-volume expansion allows us to derive the four-dimensional off-shell potential in the presence of warping and non-ISD 3-form fluxes. This corresponds to integrating out all massive Kaluza-Klein modes using the ten-dimensional equations of motion. We further propose a warped K\"ahler potential in four-dimensional $\mathcal{N}=1$ supergravity, and show that it is consistent with our ten-dimensional results. In the KKLT framework, we find that classical warping corrections, as well as mixed corrections involving non-ISD fluxes and quantum effects, are dominant, rendering the scenario effectively uncontrollable with current methods. By contrast, in LVS-like constructions these corrections are suppressed by inverse powers of the volume, specifically $\mathcal{V}^{1/2}$ or $\mathcal{V}^{1/6}$, depending on the concrete model.