Holomorphic variables in magnetized brane models with continuous Wilson lines

TL;DR

This work identifies holomorphic $ abla$-type variables in toroidal Type IIB orientifolds with magnetized D-branes and continuous Wilson lines by analyzing the action of the target-space modular group on Yukawa couplings and Wilson-line data. It shows matter fields transform as twisted fields in heterotic orbifolds and provides explicit holomorphic redefinitions for open-string matter variables $\\hat{\Phi}_{\alpha\beta}^{\vec{j}}$ and closed-string moduli, notably $\\hat{S}$ and $\\hat{T}_k$, under modular transformations and Wilson-line shifts. The authors extend the framework to non-perturbative sectors, demonstrating that D-brane instantons and gaugino condensation induce holomorphic redefinitions of closed-string moduli through their instanton measures and modular properties, ensuring consistency of the non-perturbative superpotential $W$ in holomorphic variables. The results generalize previous findings and provide a robust foundation for global D-brane model-building and inflationary scenarios in magnetized brane setups, with potential extensions to Calabi–Yau compactifications and flux backgrounds.

Abstract

We analyze the action of the target-space modular group in toroidal type IIB orientifold compactifications with magnetized D-branes and continuous Wilson lines. The transformation of matter fields agree with that of twisted fields in heterotic compactifications, constituting a check of type I/heterotic duality. We identify the holomorphic N = 1 variables for these compactifications. Matter fields and closed string moduli are both redefined by open string moduli. The redefinition of matter fields can be read directly from the perturbative Yukawa couplings, whereas closed string moduli redefinitions are obtained from D-brane instanton superpotential couplings. The resulting expressions reproduce and generalize, in the presence of internal magnetic fields, previous results in the literature.