Extrinsic Curvature Induced 2-d Gravity

2-dimensional fermions are coupled to extrinsic geometry of a conformally immersed surface in R through gauge coupling. By integrating out the fermions, we obtain a WZNW action involving extrinsic curvature of the surface. Restricting the resulting effective action to surfaces of h √ g = 1, an explicit form of the action invariant under Virasaro symmetry is obtained. This action is a sum of the geometric action for the Virasaro group and the light-cone action of 2-d gravity plus an interaction term. The central charges of the theory in both the left and right sectors are calculated.