Topological Constraints in the LARGE-Volume Scenario

TL;DR

This paper investigates how topological features of compactifications affect the stability and control of de Sitter vacua in the LARGE-volume scenario of type IIB string theory, highlighting significant constraints on model parameters.

Contribution

It provides a general bound on corrections related to topology and brane data, revealing the difficulty of achieving consistent de Sitter vacua in this framework.

Findings

Required D3 tadpole can be as high as 10^6 or more.

Controlling corrections depends strongly on topology and brane data.

Satisfying the constraints for stable vacua is likely very challenging.

Abstract

We elaborate on recent results regarding the self-consistency of de Sitter vacua in the LARGE-volume scenario of type IIB string theory. In particular, we analyze to what extent the control over warping, curvature and $g_s$ corrections depends on the topology and the orientifold/brane data of a compactification. We compute a general bound on the magnitude of these corrections which strongly constrains the D3 tadpole. The minimally required tadpole ranges from $\mathcal{O}(500)$ to $\mathcal{O}(10^6)$ or more and depends strongly on other data, in particular on the Euler number of the Calabi-Yau 3-fold, the triple-self-intersection and Euler numbers of the small divisor and the coefficient $a_s$ appearing in the non-perturbative superpotential. We give arguments suggesting that satisfying these constraints is very challenging and perhaps impossible.