Stabilizing massless fields with fluxes in Landau-Ginzburg models

TL;DR

This paper investigates how higher-order flux effects in Landau-Ginzburg models can stabilize massless fields, potentially leading to explicit Minkowski vacua without flat directions, advancing the understanding of flux configurations.

Contribution

It systematically analyzes higher-order flux effects in the $1^9$ Landau-Ginzburg model, showing stabilization of massless fields and classifying flux vectors, moving toward complete flux configuration understanding.

Findings

Several massless fields can be stabilized by flux effects.

Classification of integral flux vectors with small tadpole contribution completed.

Potential for explicit Minkowski vacua without flat directions.

Abstract

Recent work on flux compactifications suggests that the tadpole constraint generically allows only a limited number of complex structure moduli to become massive, i.e., be stabilized at quadratic order in the spacetime superpotential. We study the effects of higher-order terms systematically around the Fermat point in the $1^9$ Landau-Ginzburg model. This model lives at strong coupling and features no K\"ahler moduli. We show that, depending on the flux, several massless fields can indeed be stabilized in this fashion, and argue that this paves the way to explicit ${\mathcal N}=1$ Minkowski vacua without flat directions. Along the way, we complete the classification of integral flux vectors with small tadpole contribution. Thereby we are closing in on a future complete understanding of all possible flux configurations in the $1^9$ Landau-Ginzburg model.