Universal Properties of Type IIB and F-theory Flux Compactifications at Large Complex Structure

TL;DR

This paper demonstrates that at large complex structure, flux compactifications in type IIB and F-theory exhibit universal spectral properties with no vacua, regardless of the compactification details, extending previous findings.

Contribution

It reveals universal spectral properties and the absence of vacua in large complex structure flux compactifications, generalizing prior results to broader settings.

Findings

Spectrum of the Hessian has only three eigenvalues: 0, 2m_{3/2}^2, 8m_{3/2}^2

No vacua exist in the large complex structure region

Universal properties are independent of the compactification details

Abstract

We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory for the complex structure and axio-dilaton sector exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. We show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues ($0$, $2m_{3/2}^2$ and $8m_{3/2}^2$), independently of the number of moduli. We briefly comment on how the inclusion of K\"ahler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.