Forbidden territories in the string landscape

TL;DR

This paper investigates the limitations of moduli stabilization in type-IIB string theory on toroidal orientifolds with fluxes, showing that certain flux configurations cannot stabilize moduli while preserving supersymmetry.

Contribution

It demonstrates that Abelian worldvolume fluxes alone cannot stabilize closed string moduli in specific orientifold compactifications, highlighting fundamental constraints in string model building.

Findings

Abelian fluxes cannot stabilize moduli in these models

Certain brane wrappings are ruled out by consistency conditions

Examples with D9 and D7 branes are analyzed with specific flux configurations

Abstract

Problems of stabilizing moduli of the type--IIB string theory on toroidal orientifolds $\T^6/\Z_2$, in presence of worldvolume fluxes on various D-branes, are considered. For $Z_2$ actions, introducing either O9 or O3 planes, we rule out the possibility of moduli stabilization in a wide class of models with $\mathcal{N}=1$ supersymmetry, characterized by the type of fluxes turned on along D-brane worldvolume. Our results, in particular, imply that Abelian worldvolume fluxes can not by themselves stabilize closed string moduli, in a consistent supersymmtric model, for above orientifold compactifications. We also discuss other $Z_2$ orientifolds of $T^6$ and show that certain other brane wrappings are also ruled out by similar consistency requirements. In specific setups we consider examples with D9-branes wrapping on a complex three-torus with its world-volume fluxes taken to be semi-homogeneous bundles and D7-branes wrapping holomorphic four-cycles of the complex three-torus carrying world-volume fluxes.