Moduli stabilization in asymptotic flux compactifications

We present a novel strategy to systematically study complex-structure moduli stabilization in Type IIB and F-theory flux compactifications. In particular, we determine vacua in any asymptotic regime of the complex-structure moduli space by exploiting powerful tools of asymptotic Hodge theory. In a leading approximation the moduli dependence of the vacuum conditions are shown to be polynomial with a dependence given by sl(2)-weights of the fluxes. This simple algebraic dependence can be extracted in any asymptotic regime, even though in nearly all asymptotic regimes essential exponential corrections have to be present for consistency. We give a pedagogical introduction to the sl(2)-approximation as well as a detailed step-by-step procedure for constructing the corresponding Hodge star operator. To exemplify the construction, we present a detailed analysis of several Calabi-Yau three- and fourfold examples. For these examples we illustrate that the vacua in the sl(2)-approximation match the vacua obtained with all polynomial and essential exponential corrections rather well, and we determine the behaviour of the tadpole contribution of the fluxes. Finally, we discuss the structure of vacuum loci and their relations to several swampland conjectures. In particular, we comment on the realization of the so-called linear scenario in view of the tadpole conjecture.

Automated summary

We propose a new strategy for studying complex-structure moduli stabilization in Type IIB and F-theory flux compactifications. By utilizing the tools of asymptotic Hodge theory, we determine vacua in any asymptotic regime of the complex-structure moduli space. In a leading approximation, we find that the moduli dependence of the vacuum conditions follows a polynomial behavior with a dependence given by sl(2)-weights of the fluxes. We provide a pedagogical introduction to the sl(2)-approximation and a step-by-step procedure for constructing the corresponding Hodge star operator. Our analysis of Calabi-Yau examples demonstrates the accuracy of the sl(2)-approximation and allows us to determine the behavior of the fluxes' tadpole contribution. Furthermore, we discuss the structure of vacuum loci and their relationship to swampland conjectures, specifically the realization of the linear scenario in view of the tadpole conjecture.