Kaehler Metrics and Yukawa Couplings in Magnetized Brane Models

TL;DR

This work develops a field-theoretic framework to derive the four-dimensional effective action for magnetized D9-brane configurations by performing a Kaluza-Klein reduction of 10D ${\cal N}=1$ SYM on toroidal backgrounds. Twisted open strings, arising from branes with different magnetic fluxes, are analyzed to obtain explicit Kähler metrics and Yukawa couplings, with moduli dependence kept through the internal integrals and normalization factors fixed by holomorphy of the superpotential. The authors show that the resulting Kähler metrics for twisted and untwisted sectors reproduce known string-theory results in the appropriate limits, and they provide holomorphic Yukawa couplings that determine the proper normalization. The approach offers a practical, consistent method for connecting magnetized brane models to low-energy data and can be extended to more general compactifications.

Abstract

Using the field theoretical approach introduced by Cremades, Ibanez and Marchesano for describing open strings attached to D9 branes having different magnetizations, we give a procedure for determining the Kaehler metrics of those open strings in toroidal compactifications.