Perturbation of pulsating strings

We discuss semiclassical quantization of circular pulsating strings in ( text {AdS}_3 times text {S}^3 ) background with and without the Neveu-Schwarz–Neveu-Schwarz (NS–NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.