Neumann-Rosochatius system for strings in ABJ model

Abstract

Abstract Neumann-Rosochatius system is a well known one dimensional integrable sys- tem. We study the rotating and pulsating string in AdS4 × ℂℙ3 with a B NS holonomy turned on over ℂℙ1 ⊂ ℂℙ3, 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 a deformed Neumann-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 × ℂℙ3 with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along ℂℙ3.