Engineering Small Flux Superpotentials and Mass Hierarchies

TL;DR

This paper explores how to systematically stabilize complex structure moduli in Type IIB flux compactifications, achieving exponentially small superpotentials and understanding mass hierarchies through asymptotic Hodge theory.

Contribution

It introduces a method to realize and analyze small flux superpotentials and mass hierarchies near moduli space boundaries using recent mathematical results.

Findings

Vacua with exponentially small superpotentials can be systematically constructed.

Mass scales of stabilized moduli depend polynomially on the moduli due to exponential corrections.

The vacuum superpotential scale can be bounded below by the exponential of the negative D3-brane tadpole.

Abstract

We study the stabilization of complex structure moduli in Type IIB flux compactifications by using recent general results about the form of the superpotential and K\"ahler potential near the boundaries of the moduli space. In this process we show how vacua with an exponentially small vacuum superpotential can be realized systematically and understood conceptually within asymptotic Hodge theory. We distinguish two types of vacua realizing such superpotentials that differ by the mass scales of the stabilized moduli. Masses polynomially depending on the moduli arise if the superpotential contains exponential corrections whose existence is required to ensure the non-degeneracy of the moduli space metric. We use the fact that such essential corrections are controlled by asymptotic Hodge theory and have recently been constructed for all one- and two-moduli asymptotic regimes. These insights allow us to obtain new vacua near boundaries in complex structure moduli space that include Seiberg-Witten points. In these examples we find that the scale of the vacuum superpotential can be bounded from below through the exponential of the negative D3-brane tadpole.