Flux-Deformed Neumann–Rosochatius System

While the use of integrability is widely developed on \(\mathcal {N}=4\) SYM theory and \(AdS_5 \times S^5\), integrability methods are potentially applicable to other \(AdS_{n}\) backgrounds with RR flux and consequently to their dual CFTs. For instance one of the manifestations of the integrability in the case of the \(AdS_5/CFT_4\) correspondence that can be generalized is the identification of the Lagrangian describing closed strings rotating in \(AdS_5 \times S^5\) with the Neumann and the Neumann–Rosochatius integrable systems. This identification is used in this chapter to compute the dynamics of spinning and pulsating string in the \(AdS_3 \times S^3\) background deformed by the presence of a NS-NS flux. The pure NS-NS limit is studied in some detail as the behaviour of the system simplifies there.