  We examine the defect gauge theory on two perpendicular D3-branes with a 1+1
dimensional intersection, consisting of $U(1)$ fields on the D3-branes and
charged hypermultiplets on the intersection. We argue that this gauge theory
must have a magnetically charged soliton corresponding to the D-string
stretched between the branes. We show that the hypermultiplets do source
magnetic as well as electric fields, but the magnetic charges are confined if
the hypermultiplet action is canonical. Considerations of periodicity of the
hypermultiplet space lead to a nontrivial Gibbons-Hawking metric, and we show
that there is then the expected magnetic kink solution. The hypermultiplet
metric has a singularity, which we argue must be resolved by embedding in the
full string theory. Another interesting feature is that the classical field
equations have logarithmic divergences at the intersection, which lead to a
classical renormalization group flow in the action.
