We present a detailed study of the pulsating string solutions in AdS 3 × S 3 supported by both RR and NS-NS fluxes. This background has recently been proved to be integrable. We find the dispersion relation between the energy, oscillation number and other conserved charges when the NS-NS flux turned on is small. We further discuss the fate of the string solutions in pure RR and NS-NS cases.
Abstract:We derive the energy of pulsating strings as a function of adiabatic invariant oscillation number, which oscillates in S 2 κ . We find similar solutions for the strings oscillating in deformed AdS 3 . Furthermore, we generalize the result of the oscillating strings in anti-de Sitter space in the presence of extra angular momentum in (AdS 3 × S 1 ) κ .
We discuss semiclassical quantization of circular pulsating strings in AdS 3 × 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.
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We study the finite size effect of rigidly rotating and spinning folded strings in (AdS 3 × S 3 ) κ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert W -function. arXiv:1807.04601v3 [hep-th]
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