Spinning Strings on $(AdS_{5}\times S^{5})_{\eta}$ and Deformations of the Neumann Model

Abstract

Spinning strings solutions have played an important role on recent developments in the AdS/CFT correspondence. In the first part of this thesis the Neumann model is reviewed, and we explain how this integrable system appears naturally in the study of rotating strings in the AdS5 × S5 background. Then, we give brief introduction to (AdS5 × S5)η, a recently proposed integrable deformation of AdS5 × S5. Afterwards, we show that bosonic spinning strings on this background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed as a deformation of the celebrated Neumann model. For this deformed model we find the Lax representation and the analogue of the Uhlenbeck integrals.