  We analyse the renormalisation group flow for D-branes in WZW models from the
point of view of the boundary states. To this end we consider loop operators
that perturb the boundary states away from their ultraviolet fixed points, and
show how to regularise and renormalise them consistently with the global
symmetries of the problem. We pay particular attention to the chiral operators
that only depend on left-moving currents, and which are attractors of the
renormalisation group flow. We check (to lowest non-trivial order in the
coupling constant) that at their stable infrared fixed points these operators
measure quantum monodromies, in agreement with previous semiclassical studies.
Our results help clarify the general relationship between boundary transfer
matrices and defect lines, which parallels the relation between
(non-commutative) fields on (a stack of) D-branes and their push-forwards to
the target-space bulk.
