A CONTINUUM APPROACH TO 2D-QUANTUM GRAVITY FOR C-GREATER-THAN-1

Two dimensional induced quantum gravity with matter central charge c > 1 is studied by carefully treating both diffeomorphism and Weyl symme tries. It is shown that, for the gauge fixing condition R(g) (scalar c urvature) = const, one obtains a modification of the David-Distler-Kaw ai version of KPZ scaling. We obtain a class of models with real strin g tension for all values c > 1. They contain a free parameter which is , however, strongly constrained by the requirement of the non triviali ty of the model. The possible physical significance of the new model i s discussed. In particular we note that it describes smooth surfaces i mbedded in d-dimensional flat space time for arbitrary d, which is con sistent with recent numerical results for d = 3.