Asymptotic Flux Compactifications and the Swampland

TL;DR

This paper uses asymptotic Hodge theory to classify flux scalar potentials in F-theory compactifications, demonstrating the absence of de Sitter vacua at parametric control and constraining large field axion dynamics.

Contribution

It introduces a systematic classification of flux scalar potentials near boundary regions in moduli space, extending no-go theorems and analyzing large field behavior in string compactifications.

Findings

No de Sitter vacua at parametric control in studied regimes

Satisfaction of the asymptotic de Sitter conjecture near boundaries

Identification of fluxes leading to infinite series of Anti-de Sitter vacua

Abstract

We initiate the systematic study of flux scalar potentials and their vacua by using asymptotic Hodge theory. To begin with, we consider F-theory compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a classifications of all scalar potentials can be performed when focusing on regions in the field space in which one or several fields are large and close to a boundary. To exemplify the constraints on such asymptotic flux compactifications, we explicitly determine this classification for situations in which two complex structure moduli are taken to be large. Our classification captures, for example, the weak string coupling limit and the large complex structure limit. We then show that none of these scalar potentials admits de Sitter vacua at parametric control, formulating a new no-go theorem valid beyond weak string coupling. We also check that the recently proposed asymptotic de Sitter conjecture is satisfied near any infinite distance boundary. Extending this strategy further, we generally identify the type of fluxes that induce an infinite series of Anti-de Sitter vacua, thereby generalizing the well-known Type IIA settings. Finally, we argue that also the large field dynamics of any axion in complex structure moduli space is universally constrained. Displacing such an axion by large field values will generally lead to severe backreaction effects destabilizing other directions.