Conformal invariant strings with extrinsic curvature action

We study a string theory which is exclusively based on extrinsic curvature action. It is a tensionless string theory because the action reduces to perimeter for the flat Wilson loop. We are able to solve and quantize this high-derivative nonlinear two-dimensional conformal field theory. The absence of conformal anomaly in quantum theory requires that the space-time should be 13-dimensional. We have found that all particles, with arbitrary large spin, are massless. This pure massless spectrum is consistent with the tensionless character of the theory and we speculate that it may describe unbroken phase of standard string theory.