  We compute the dilatation operator for local "open string" operators situated
at the interface of a certain supersymmetric defect version of $\mathcal{N}=4$
super-Yang-Mills theory. This field theory is dual to a probe D5-brane
intersecting a stack of D3-branes where the number of D3-branes can change
between the two sides the interface. DeWolfe and Mann obtained the dilation
operator in the special case of an equal number of D3-branes. Using a
combination explicit field theory calculations and integrability considerations
we are able to extend this result to the general case.
