Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation

The generalized Weierstrass representation for surfaces in R3 is used to study quantum effects for strings governed by Polyakov-Nambu-Goto action. Correlators of primary fields are calculated exactly in one-loop approximation for the pure extrinsic Polyakov action. Geometrical meaning of infrared singularity is discussed. The Nambu-Goto and spontaneous curvature actions are treated perturbatively.