Neumann-Rosochatius system for strings in ABJ Model

TL;DR

This paper explores the integrability of rotating and pulsating strings in the ABJ background, revealing that their equations reduce to a deformed Neumann-Rosochatius system and analyzing their conserved charges and finite size effects.

Contribution

It demonstrates the integrability of string equations in the ABJ background and derives relations among conserved charges and energy for specific string configurations.

Findings

String equations are integrable in the ABJ background.

Scaling relations among conserved charges are established.

Finite size effects for dyonic giant magnons are discussed.

Abstract

Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $AdS_4 \times \mathbb{CP}^3$ with a $B_{\rm{NS}}$ holonomy turned on over $\mathbb{CP}^1 \subset \mathbb{CP}^3$, or the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the string equations of motion in both cases are integrable and the Lagrangians reduce to a form similar to that of deformed Neuman-Rosochatius system. We find out the scaling relations among various conserved charges and comment on the finite size effect for the dyonic giant magnons on $R_{t}\times \mathbb{CP}^{3}$ with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along $\mathbb{CP}^{3}$.