  An exact renormalization group equation is written down for the world sheet
theory describing the bosonic open string in general backgrounds. Loop variable
techniques are used to make the equation gauge invariant. This is worked out
explicitly up to level 3. The equation is quadratic in the fields and can be
viewed as a proposal for a string field theory equation. As in the earlier loop
variable approach, the theory has one extra space dimension and mass is
obtained by dimensional reduction. Being based on the sigma model RG, it is
background independent.
  It is intriguing that in contrast to BRST string field theory, the gauge
transformations are not modified by the interactions up to the level
calculated. The interactions can be written in terms of gauge invariant field
strengths for the massive higher spin fields and the non zero mass is essential
for this. This is reminiscent of Abelian Born-Infeld action (along with
derivative corrections) for the massless vector field, which is also written in
terms of the field strength.
