Role of Short Distance Behavior in Off-Shell Open-String Field Theory

A recent proposal for a background independent open string field theory is studied in detail for a class of backgrounds that correspond to general quadratic boundary interactions on the world-sheet. A short-distance cut-off is introduced to formulate the theory with a finite number of local and potentially unrenormalizable boundary couplings. It is shown that renormalization of the boundary couplings makes both the world-sheet partition function and the string field action finite and cut-off independent, although the resulting string field action has an unpalatable dependence on the leading unrenormalizable coupling.