Open string modes at brane intersections

We study systematically the open string modes of a general class of BPS intersections of branes. We work in the approximation in which one of the branes is considered as a probe embedded in the near-horizon geometry generated by the other type of branes. We mostly concentrate on the D3-D5 and D3-D3 intersections, which are dual to defect theories with a massive hypermultiplet confined to the defect. In these cases we are able to obtain analytical expressions for the fluctuation modes of the probe and to compute the corresponding mass spectra of the dual operators in closed form. Other BPS intersections are also studied and their fluctuation modes and spectra are found numerically.