  The exact renormalization group is applied to the world sheet theory
describing bosonic open string backgrounds to obtain the equations of motion
for the fields of the open string. Using loop variable techniques the equations
can be constructed to be gauge invariant. Furthermore they are valid off the
(free) mass shell. This requires keeping a finite cutoff. Thus we have the
interesting situation of a scale invariant world sheet theory with a finite
world sheet cutoff. This is possible because there are an infinite number of
operators whose coefficients can be tuned. This is in the same sense that
"perfect actions" or "improved actions" have been proposed in lattice gauge
theory to reproduce the continuum results even while keeping a finite lattice
spacing.
