Small flux superpotential in F-theory compactifications

TL;DR

This paper explores the possibility of achieving exponentially small superpotentials in F-theory compactifications by extending methods from Type IIB flux models, analyzing flux choices, mirror symmetry, and instanton effects.

Contribution

It introduces a simplified flux superpotential framework in F-theory and applies mirror symmetry to study instanton corrections and vacuum solutions.

Findings

Restricted G_4-flux choices lead to supersymmetric vacua with flat directions.

Mirror symmetry techniques determine instanton corrections to the potential.

Detailed analysis of a specific model's vacuum solutions.

Abstract

We investigate whether a class of models describing F-theory compactifications admits a specific type of flux vacua with an exponentially small vacuum expectation value of the superpotential, by generalizing a method recently developed in Type IIB flux compactifications. First we clarify that a restricted choice of $G_4$-flux components reduces a general flux superpotential into a simple form, which promotes the existence of supersymmetric vacua with one flat direction at the perturbative level. Then we utilize the techniques of mirror symmetry to determine one-instanton corrections to the potential and investigate in detail the vacuum solutions of a particular model.