  We study the dressing of operators and flows of corresponding couplings in
models of {\it embedded} random surfaces. We show that these dressings can be
obtained by applying the methods of David and Distler and Kawai. We consider
two extreme limits. In the first limit the string tension is large and the
dynamics is dominated by the Nambu-Goto term. We analyze this theory around a
classical solution in the situation where the length scale of the solution is
large compared to the length scale set by the string tension. Couplings get
dressed by the liouville mode (which is now a composite field) in a non-trivial
fashion. However this does {\it not} imply that the excitations around a
physical ``long string" have a phase space corresponding to an extra dimension.
In the second limit the string tension is small and the dynamics is governed by
the extrinsic curvature term. We show, perturbatively, that in this theory the
relationship between the induced metric and the worldsheet metric is
``renormalized", while the extrinsic curvature term receives a non-trivial
dressing as well. This has the consequence that in a generic situation the
dependence of couplings on the physical scale is different from that predicted
by their beta functions.
