The semi-classical energy of closed Nambu-Goto strings
  We compute semi-classical 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 semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond. 
Marek Kozo\v{n}, Jochen Zahn
hep-th math-ph math.MP