Moduli stabilization with open and closed string fluxes

TL;DR

This paper tackles the long-standing problem of stabilizing all closed-string moduli in a controllable, calculable setting. It shows that a combination of open-string magnetic fluxes on magnetized $D9$ branes in a $T^6/\mathbb{Z}_2$ orientifold can fix the complex structure and Kahler moduli under SUSY constraints, while perturbative closed-string 3-form fluxes stabilize the dilaton-axion, yielding full moduli stabilization with a perturbative string coupling. The authors construct explicit tadpole-consistent models (A, B, C) with detailed flux choices, demonstrating fixed moduli (e.g., $\tau^{ij}=i\delta^{ij}$ and $J_{i\bar{i}}=(2\pi)^2\alpha'/2$ in parts of the setup) and showing how tadpoles constrain flux values and the allowed vacua. They further show that radii can be made arbitrarily large (or certain dimensions large in a T-dual picture) while keeping the moduli fixed and the coupling perturbative, and they discuss extensions to include open-string moduli, gauge symmetry breaking, and non-supersymmetric vacua. Overall, the work provides a concrete, string-theoretic mechanism for complete moduli stabilization with calculable spectra and couplings, enhancing the prospects for string phenomenology and model-building in flux backgrounds.

Abstract

We study the stabilization of all closed string moduli in the T^6/Z_2 orientifold, using constant internal magnetic fields and 3-form fluxes that preserve N=1 supersymmetry in four dimensions. We first analyze the stabilization of Kahler class and complex structure moduli by turning on magnetic fluxes on different sets of D9 branes that wrap the internal space T^6/Z_2. We present explicit consistent string constructions, satisfying in particular tadpole cancellation, where the radii can take arbitrarily large values by tuning the winding numbers appropriately. We then show that the dilaton-axion modulus can also be fixed by turning on closed string constant 3-form fluxes, consistently with the supersymmetry preserved by the magnetic fields, providing at the same time perturbative values for the string coupling. Finally, several models are presented combining open string magnetic fields that fix part of Kahler class and complex structure moduli, with closed string 3-form fluxes that stabilize the remaining ones together with the dilaton.

Figures (2)

• Figure 1: T-duality along the vertical axis $u_{2i}$. The $D$-brane dual to a magnetized brane forms an angle $\frac{\pi}{2}-\phi$ with respect to the vertical axis. The orientifold plane, T-dual to an $O3$-plane, sits along the vertical axis.
• Figure 2: Example of a brane at angle with its orientifold image and antibrane. The $O$-plane is situated on the vertical axis.