Semiclassical energy of closed Nambu-Goto strings

We compute semiclassical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semiclassical approximation, the spectrum of physical excitations contains modes that are unphysical nonperturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond.