Solitons on intersecting 3-branes

We consider a system consisting of a pair of D3 branes intersecting each other along a line such that half of the 16 supersymmetries are preserved. We then study the existence of magnetic monopole solutions corresponding to a D1-brane suspended between these D3 branes. We consider this problem in the zero slope limit where the tilt of the D3-branes is encoded in the uniform gradient of the adjoint scalar field. Such a system is closely related to the non-abelian flux background considered originally by van Baal. We provide three arguments supporting the existence of a single magnetic monopole solution. We also comment on the relation between our construction and a recent work by Mintun, Polchinski, and Sun