Notes on higher-derivative conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string

A bstract I investigate the higher-derivative conformal theory which shows how Nambu-Goto and Polyakov strings can be told apart. Its energy-momentum tensor is conserved, traceless but does not belong to family of unit operator. To implement invariance in such a case develop new technique that explicitly accounts for quantum equation motion results singular products. show transformations generated by nonprimary form Lie algebra with central extension path-integral formalism gives logarithmically divergent contribution charge. demonstrate logarithmic divergence canceled string susceptibility reproduce previously obtained deviation from KPZ-DDK at one loop.