A note on spin chain/string duality

TL;DR

The paper extends the spin-chain/string duality in AdS/CFT beyond the Neumann case by analyzing a more general spin-chain sigma-model solution that maps to the Neumann-Rosochatius integrable system on the string side. It derives elliptic-function solutions for two-spin configurations and expresses conserved quantities in terms of elliptic data, illustrating how the NR dynamics captures a broader class of rotating-string configurations. By including previously neglected contributions and suitable redefinitions, it shows exact one-loop agreement between spin-chain and rotating-string results, providing a nontrivial check of the duality. The work also points toward extensions to the Inozemtsev long-range spin chain and higher-order matching, reinforcing the robustness of the spin-chain/string correspondence in semiclassical regimes.

Abstract

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.