A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

Abstract In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in R 3 , it was previously shown that restricting ourselves to surfaces with h √ g = 1, where h is the mean scalar curvature and g is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces which is the intrinsic curvature analog of the WZNW action is constructed in this article. This action turns out to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action has conserved SL (2, C ) currents. This allows us to quantize this theory along the lines of the WZNW model. The quantum theory on h √ g = 1 surfaces in R 3 is shown to be in the same universality class of the intrinsic 2-d gravity theory.