Moduli Stabilization in Asymptotic Flux Compactifications

TL;DR

This paper introduces a systematic method using asymptotic Hodge theory to analyze complex-structure moduli stabilization in flux compactifications, providing algebraic tools to identify vacua in various asymptotic regimes.

Contribution

It develops a novel algebraic approach based on sl(2)-weights for studying moduli stabilization, applicable even with exponential corrections, and demonstrates its effectiveness on Calabi-Yau examples.

Findings

Vacua can be approximated using polynomial dependence in asymptotic regimes.

The sl(2)-approximation aligns well with full solutions including exponential corrections.

Insights into flux tadpole contributions and swampland conjectures are provided.

Abstract

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.