Renormalization of dual models

A regularization and renormalization program for dual models in the critical dimension is discussed. The counterterms required for regularization are shown to be multiple insertions of zero-momentum dilatons. A heuristic summation of all such insertions leads to a slope and coupling-constant renormalization, and also to an intercept shift. The faults of the heuristic argument are discussed, and it is proved to lowest order and conjectured in general that the correct treatment leads to no intercept shift but only to renormalizations.