action on WZW boundary states. Their analysis is, however, semiclassical, and they do not try to define the operator in the bulk, nor away from its critical point. The connection between quantum monodromy matrices and boundary flows has also been discussed by Bazhanov [*et.al.*]{}  [@Bazhanov:1994ft] in the context of minimal models. Their conformal perturbation scheme could be used in the Kondo problem, though it would force one to abandon the explicit $su(2)$ symmetry of the flow.[^4] Finally, other discussions of boundary states for D-branes with non-abelian backgrounds switched on can be found in refs. [@Ishibashi:1998ni] and [@Pesando:2003ww].

The plan of this paper is as follows : in section 2 we discuss the push-forward of D-brane fields to the bulk of the target space, and the corresponding push-forward of the boundary transfer matrix to a loop operator in the worldsheet bulk. We also explain the difference between conformal, chiral and topological defects. In section 3 we introduce the symmetric defect lines of the WZW model, and give a semiclassical argument that identifies their fixed points. In section 4 we regularise these defects, so as to respect a number of classical symmetries, and expand the regularised loop operator up to fourth order 