Neumann-Rosochatius integrable system for strings on AdS_4 x CP^3

TL;DR

This work develops a Neumann-Rosochatius reduction for classical strings on $AdS_4\times\mathbb{CP}^3$, deriving an NR system with CP$^3$-specific embedding constraints and revealing how two angular momenta can be realized in $\mathbb{CP}^3$. By solving the NR system under a two-angular-momenta ansatz, explicit giant magnon and single spike solutions are constructed, expressed through elliptic functions, and their finite-size corrections are computed. In the infinite-volume limit, the dispersion relations recover familiar GM/SS forms, and the finite-size analyses produce results that align with corresponding AdS$_5\times$S$^5$ analyses, after appropriate identifications. The results provide a concrete link between NR integrability in $AdS_4/CFT_3$ (ABJM) and gauge-theory operators, while suggesting avenues for comparison with all-loop Bethe Ansatz and S-matrix frameworks.

Abstract

We use the reduction of the string dynamics on AdS_4 x CP^3 to the Neumann-Rosochatius integrable system. All constraints can be expressed simply in terms of a few parameters. We analyze the giant magnon and single spike solutions on R_t x CP^3 with two angular momenta in detail and find the energy-charge relations. The finite-size effects of the giant magnon and single spike solutions are analyzed.