  The influence of closed string moduli on the D-brane moduli space is studied
from a worldsheet point of view. Whenever a D-brane cannot be adjusted to an
infinitesimal change of the closed string background, the corresponding exactly
marginal bulk operator ceases to be exactly marginal in the presence of the
brane. The bulk perturbation then induces a renormalisation group flow on the
boundary whose end-point describes a conformal D-brane of the perturbed theory.
We derive the relevant RG equations in general and illustrate the phenomenon
with a number of examples, in particular the radius deformation of a free boson
on a circle. At the self-dual radius we can give closed formulae for the
induced boundary flows which are exact in the boundary coupling constants.
