Neumann-Rosochatius system for rotating strings in $AdS_3 \times S^3\times S^3\times S^1$ with flux

TL;DR

This paper constructs an integrable Neumann-Rosochatius model for strings in a fluxed $AdS_3 imes S^3 imes S^3 imes S^1$ background, analyzing rotating string solutions and their properties.

Contribution

It develops a deformed NR integrable model tailored for strings in fluxed backgrounds, extending the classical NR system to include flux effects.

Findings

Deformed NR model captures flux effects on string dynamics

Analysis of rigidly rotating spiky strings in the deformed model

Insights into spike rounding-off with non-zero angular momentum

Abstract

Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with 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 $S^3\times S^1$. We further present some mathematical speculations on the rounding-off nature of the spike in the presence of non-zero angular momentum $J$ in $S^1$.