The Field Theory of Intersecting D3-branes

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.