Open strings in the system D5/D9

We construct the six-dimensional Lagrangian for the massless twisted open strings with one end-point ending on a stack of D5 and the other on a stack of D9 branes, interacting with the gauge multiplets living respectively on the D5 and D9 branes. It is first obtained by uplifting to six dimensions the four-dimensional Lagrangian of the N=2 hypermultiplet and manifestly exhibits an SU(2) symmetry. We show by an explicit calculation that it is N=1 supersymmetric in six dimensions and then we check various terms of this Lagrangian by computing string amplitudes on the disk. Finally, starting from this Lagrangian and assuming the presence of non-zero magnetic fluxes along the extra compact dimensions, we determine the spectrum of the Kaluza-Klein states which agrees with the corresponding one obtained from string theory in the field theory limit.