# K\"ahler moduli stabilization in semi-realistic magnetized orbifold models

## TL;DR

This paper explores how magnetic fluxes and D-brane instantons can stabilize K"ahler moduli in semi-realistic magnetized orbifold models, advancing understanding of moduli stabilization in string compactifications.

## Contribution

It demonstrates concrete D-brane configurations on orbifolds where instantons successfully stabilize K"ahler moduli, including the origin of small superpotential constants.

## Key findings

- D-brane instantons can stabilize K"ahler moduli in specific models
- Configurations explain the small constant term in the superpotential
- Successful stabilization within Pati-Salam and D7-brane models

## Abstract

We study K\"ahler moduli stabilizations in semi-realistic magnetized D-brane models based on $ Z_2\times Z_2'$ toroidal orbifolds. In type IIB compactifications, 3-form fluxes can stabilize the dilaton and complex structure moduli fields, but there remain some massless closed string moduli fields, K\"ahler moduli. The magnetic fluxes generate Fayet-Iliopoulos terms, which can fix ratios of K\"ahler moduli. On top of that, we consider D-brane instanton effects to stabilize them in concrete D-brane models and investigate the brane configurations to confirm that the moduli fields can be stabilized successfully. In this paper, we treat two types of D-brane models. One is based on D9-brane systems respecting the Pati-Salam model. The other is realized in a D7-brane system breaking the Pati-Salam gauge group. We find suitable configurations where the D-brane instantons can stabilize the moduli fields within both types of D-brane models, explaining an origin of a small constant term of the superpotential which is a key ingredient for successful moduli stabilizations.