Holomorphic variables in magnetized brane models with continuous Wilson lines

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.