Deformed Neumann model from spinning strings on (AdS_5 x S^5)_\eta

TL;DR

This paper introduces a new integrable system that models bosonic spinning strings on an ta-deformed AdS_5 x S^5 background, extending the classical Neumann model with a Lax representation and conserved quantities.

Contribution

It presents a novel finite-dimensional integrable system as a deformation of the Neumann model, capturing the dynamics of spinning strings in a deformed AdS background.

Findings

Established the Lax representation for the deformed model

Derived the analogue of Uhlenbeck integrals for the system

Connected string solutions to a finite-dimensional integrable system

Abstract

We show that bosonic spinning strings on the \eta-deformed AdS_5 x S^5 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.