Perturbation of pulsating strings

Abstract

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. Contents

On N-spike strings in conformal gauge with NS-NS fluxes

“…All of it started as the 'Giant Magnon' dispersion relation was proposed in [44], which turned out to have non-periodic contribution in the momentum as the periodicity is explicitly spoiled by the flux. Subsequently finite-gap solutions were proposed in [49,50] and a large class of folded [51], rotating [52,53,54], pulsating [55,56] and GKP-like multi-spike [57,58] strings have been studied in the literature. Also, well known Neumann-Rosochatius dynamical model of strings has been generalised to AdS 3 × S 3 with NS-NS fluxes together with relevant classical solutions [59,60,61] and one-loop quantization [62] being elucidated in a large number of papers.…”

Pulsating strings with mixed three-form flux

“…Integrability has also been shown to remain a symmetry of general string backgrounds that support a mixture of R-R and NS-NS three-form fluxes [12]. This discovery has led to an insightful view of many features of the AdS 3 /CFT 2 correspondence in the presence of mixed fluxes [13]- [29]. One of these developments was the demonstration that the sigma-model of type IIB closed strings spinning in AdS 3 ×S 3 with mixed fluxes corresponds to an integrable deformation of the Neumann-Rosochatius mechanical system [30].…”

“…Using condition (29) it is immediate to check that one of the roots of the polynomial (22) is given by µ 0 = k 2 1 . The remaining roots are given by…”

On multi-spin classical strings with NS-NS flux

“…Once the integrability of the background was proved, a modified 'Giant Magnon' dispersion relation was proposed in [34], which turned out to have non-periodic contribution in the momentum. Subsequently finite-gap equations were proposed [44,45] and a large class of folded [46], rotating [47,48], pulsating [49,50] and GKP-like multi-spike [51] strings were studied in an attempt to formalise the AdS/CFT dictionary to have a hint of the relevant operators. In fact the presence of the fluxes seem to have modified scaling relations between conserved charges considerably to the leading order via terms depending on the parameter b.…”