Anomalies generated by extrinsic curvature

On the classical level, the embedding of a two-dimensional string in a d-dimensional space induces a natural Weyl operator. It is shown, however, that for d ≥ 4 the corresponding quantum theory is ill-defined. The anomalies of the effective action require the presence of additional degrees of freedom - the theory cannot be specified exclusively in terms of the embedding. (orig.)