Neumann-Rosochatius system for rotating strings in AdS3 × S3 × S3 × S1 with flux

Abstract

We wish to construct an integrable Neumann-Rosochatius (NR) model of strings in AdS3 × S3 × S3 × S1 supported by pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations, which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only in S3 × S1. We further present a quantitative study on the rounding-off nature of the spike in the presence of non-zero angular momentum J in S1.